Hyper new here myself, but...your questions are a BIT vague. Still, best answer I can give with my extremely limited knowledge:
TL;DR up front:
Duelist: Strong, quick, heals (spot and AOE), probably the "designated party healer" but can single target well, most straightforward and beginner friendly, decent damage. Reactive healer.
Sentinel: Sustained, efficient HoT rolling, armor buffing, probably the "designated tank healer", nice and tanky when you need to solo or "emergency off-tank". Proactive healer.
Warlord: Efficient song rolling to maintain party buffs and minimize downtime. Buffer with a minor in healing. Probably the most complex to use well, but may be the most powerful when mastered.
Disclaimer: Anyone can say this is wrong or that I'm too green to answer this question...but c'mon, you've left this poor fellow hangin' for 4, almost 5 months. XD
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Duelist has the fastest/most spamable heal in the game (Patch at level 6 has a 1 sec cast and no CD), and the most efficient party heal (Triage, the higher level one, is mana efficient the more people it heals, so healing a fully party who all have damage, it's the most efficient and potent heal in the game). They learn a lot of attack spells, but their damage is still somewhat meh (all Healer/Supporters are), but if you wanted to load your bar with attacks and use Patch for general healing and First Aid for when you have very low health (longish CD but heals more the lower the target's health is, making it efficient when used at low HP values), you can make a half-decent attack build...for soloing...still not great, but it's there if you're into that. Duelist seems to be the best burst healer in the game, and CAN be a mana efficient healer when played well. Also gets Stim which you can use as stamina regen, so this is your Innervate (WoW Druid) or Lucid Dreaming (all FFXIV healers) type ability. Duelists can solo decently, but it's slow (though this may be true for everyone) with a measure of safety as long as you watch for adds, etc. Their healing is effcient and useful for a group, with the most efficient party heal as I said above, and they have a few skills that can enhance allies' attacks, like Serrated Blades or Weak Point, though they're nothing to write home about (far as I can tell), they're there. Also, while Sentinel can taunt enemies and armor up to survive, Duelist is the only healer with a threat reduction ability to shed threat. They make me think of Holy Paladins in the Wrath era of WoW with their strong, quick, and reactive heals. I've also heard people likening it to EQ Shamans, though I never played one of those, so defer to them on it.
Warlord's got the most limited healing options of the three, with First Aid (mentioned above) and its group healing over time song, which is efficient but doesn't do well in burst heal situations (where you need a lot of healing in a short time). Conversely, best party buffer in the game, I think(?), with the party stam regen (always good for camps or dungeon crawls), healing regen song, attack speed (or accuracy?) song to increase party damage on the enemy, etc. It also has an AOE debuff (which the other two do not) against enemies, and has single target (and I think higher level AOE?) CC in the form of fear. Though fear CAN be dangerous, it's an option in a pinch or if the party doesn't have a CC/the CC being used isn't landing/sticking on the enemy for whatever reason. Warlords are great at reducing downtime, but really shine in a party environment. People tend to say these are a lot like EQ Bards. I played EQ for all of a month (being a kid without a way to pay a subscription fee and only getting the free mont that came with my game at the time), and most MMOs just don't have a real buffer/supporter role or classes...so I'll defer to the wisdom of the masses and say it here.
You didn't ask about it, but, for the purposes of completeness:
Sentinel is the most overall defensive of the healers. Their heals aren't as bursty as a Duelist but are efficient heal over times. Their buffs/debuffs are largely aimed at having self or allies take less damage, either bolstering armor or reducing enemy damage dealt. They also have 5 more points of armor weight (can use slightly better armor) than the other two, can fortify it more from their buffs, and are the only healer with the interesting option of a taunt, which with their heavier armor can potentially come in clutch. They seem like they do lower damage, making soloing more slow, but on the other hand, because they have more armor and efficient HoTs, they can probably do so reliably and consistently, if slowly, outlasting what they choose to fight. Probably most like EQ Clerics/WoW Resto Druid (HoTs for days, Bear form for emergency tanking) of the bunch. I didn't play EQ but for a month (was a kid with no credit card for a subscription fee at the time XD), so can't speak to fhe former, but I can speak to the latter, and think the rolling HoTs and emergency tanking of WoW Druids is probably a decently applicable comparison.
Grouping:
They're all good healers, though have different focuses. Duelist is good at burst healing and party (AOE) healing and decent at damage itself, but nothing compared to a DD class; may be the easiest to heal since they have direct and quick heals for reactive gameplay. Good in small or ad hoc groups since they can sorta adjust to the needs of the party in limited ways (e.g. if you have 2 tanks, 2 other healers, yourself, and one DD, you can KIND of try to sub into being a DD-lite...not well, but meh). Sentinel is good at single target (Tank) healing and buffing party defenses and sustain (HoTs); efficient and sustained healing, though a bit more proactive/set-up than Duelist, and able to survive and even tank for short times if needed, though short should be emphasized. Warlord is good at party buffing and enemy debuffing, it's capable of healing as well, but has more limited tools for that so has to be used carefully, but its party damage buffs should have the enemies dying faster than the other two. Probably the best for camps since they decrease downtime, and they play well with other healers since they boost the other healer's abilities as well (Duelist can do this with Stim, which is stronger stamina regen but single target only).
Soloing:
They're all going to be slow at it, since the game isn't hyper-solo friendly. That said... Duelist seems to have a lot of damage options so lots of abilities to cycle through cutting down the enemy HP bar and, importantly, Patch (also Triage, but that's a party heal) having a short cast time and no recast CD means they can run and heal themselves while running. This can be useful if you have to run becase an add joined the fight or you realize the enemy you attacked is too strong and need to make a tactical withdraw. (To put it another way: Duelists are probably the best at RUNNING AWAY if the situation turns bad. Which isn't an insult, sometimes that IS the most prudent thing to do.) Also has an execute (only usable when enemy is less than 50% health and does more damage the lower their health) which is...an..."interesting"...choice for a healer. Sentinel's armor and buffs and efficient, sustained healing means it probably won't die unless you've picked off WAY more than you can chew...but few attacks means it will be even slower at killing things. Trade higher risk for lower reward. But if slow and steady is your style, probably works pretty well. Warlord's buffs and debuffs work on themselves as well as a party...but only at 1/6th the effectiveness since you only have your one self to buff. Probably less than 1/6th since your damage isn't equal to a DD. They do have a lot of options to slot out and try in different arrangements, though, and less downtime between pulls.
In general:
Note all healers have access to the same weapons (1h sword, 1h axe, 2h quarterstaff, ranged crossbow). While I personally am not a huge fan of crossbows (would love to be able to use shortbows since I like archery and the idea of a healer using a bow), one nice thing is all your attack abilities...work with the crossbow. Meaning you can fight from range if you want, just note the range of your spells so you're still in range of the people that need healing. Embers Adrift is a low fantasy setting, so you can throw bandages 8 meters, not cast a healing magic spell from 40 meters away.
But it's a nice touch that you can pull back a bit in cases of, for example, enemies with AOE damage, and pew pew with your crossbow.
It completely depends on what you want to do and what you like. I tend to like being a pure healer and was pretty set on Sentinel, but reading the descriptions, I realized that Duelist looked more my speed becuase I like having a heal that's always available and can be spammed at need (Patch) and tend to enjoy more reactive, adabtable healing which the Duelist has vs the Sentinel's proactive style that is powerful and efficient in an organized group situation, but less good in "SHTF" situations. It also seems that the damage might be a bit more useful if I have to solo and the strong and spamable heals could be useful for traveling or getting out of dangerous situations. I was worried it was "the solo healer that groups wouldn't want", but (a) groups seem to take whatever is available most of the time anyway and (b) it seems to be a fully capable healer and have the best party heal in the game anyway. So I'm not so worried about not having a party spot. I also remember playing a Healadin in WoW back in the day and loved the "heals for dayz" style of quick and strong heals, so this seemed to suit me best.
Sentinel is still a great choice for people that want to "turtle and the hare" slow and steady their way, and they're obviously always welcome in groups. If there end up being big raids at some point, they'll probably be in the tank party as the main tank healers, and there are some interesting options there with off-tanking potential (in smaller group content). All in all, it's a solid choice as well, just wasn't mine. But for fans of the old school Cleric type healer, this one can't be beat. While all the healers are good, and most balanced parties will probably have two, Sentinels absolutely have a solid spot because of their defensive buffs and, like I say, if there's ever large group content, they'll likely feature prominently due to their efficient and sustained healing and defensive boosting abilities.
And Warlord is a storng contender for camps/xp farming parties, and useful as a secondary healer in general. I've heard things about it soloing, but can't speak to them myself. It SEEMS less focused on that, but maybe there's something I'm missing. (I'm only even posting all this because no one's given you an answer yet). Always welcome in groups, lots of buffs, has the Bard "juggle/upkeep songs for best results" gameplay that a lot of people loved and have missed since most modern MMOs just don't fill that niche in any way/don't have classes that even DO that. Probably the least solo friendly of the bunch, but groups and your co-healer (whether Sentinel or Duelist) will like having you around, clutch situations you can roll the dice with fear and potentially safe (or doom) parties, and the downtime cutting from stamina and health regen songs will be a boon to any party.
Based on gameplay:
I'm still really new, and only have Duelist to speak of, and only at a low level. But so far, here's my experience with it's gameplay:
I really like Patch. Feels good being able to use Screen on my tank if surprise adds join the fight, use the base purple attack (that all healers have) to cut the enemy's armor down, use Patch to keep the tank's health stable or quickly heal/save a DD or other healer who got agro until the tank can pull off of them, and having First Aid in my back pocket if the fight drags on and I need to switch to higher efficiency single target healing. The damage isn't huge, but is decent when fighting single chevron, at level enemies, and there are some utility attacks/debuffs/buffs that could be useful in different situations if I want to mix things up. So...decent damage, some interesting abilities, responsive and direct heals that are easy to understand and execute, and the ability to be efficient if needed. But, agian, my experience is VERY limited. But I think this general playstyle will be debuff the enemies a bit, spot heal people at need with Patch, party heal with Triage if needed (3 or more targets - remember that heals ARE ALSO REVIVES in this game, so Triage could potentially bring up to 5 downed people back into the fight), and swap to efficient healing via First Aid if really necessary, using Stim to manage stamina. Soloing is basically load up on attack abilities and abuse Patch to keep yourself in the action and/or to heal as you run in case you bite off more than you can chew. I think Duelist MAY be the easiest healer to understand its kit and execute healing duties well since it's straightforward and Patch/Triage short cast time (and Patch's no CD) make it very beginner friendly to recover from mistakes ("Oops! I used Patch on the wrong person! Guess I wasted 10% stamina but I can cast it again on the person in actual need and save them anyway!" is far less devastating than "Oops! I used First Aid on the wrong person...and now can't heal them for 10 seconds!")
Talking to people in the other subclasses, they ALL seem to have things going for them. So it's really more about what you want and what playstyle you like best. But as far as group healing, which is the big thing in this game:
Duelist: Strong, quick, heals (spot and AOE), probably the "designated party healer" but can single target well, most straightforward and beginner friendly, decent damage. Reactive healer.
Sentinel: Sustained, efficient HoT rolling, armor buffing, probably the "designated tank healer", nice and tanky when you need to solo or "emergency off-tank". Proactive healer.
Warlord: Efficient song rolling to maintain party buffs and minimize downtime. Buffer with a minor in healing. Probably the most complex to use well, but may be the most powerful when mastered.
