They are vastly different in how they work, I tried them all this xpac
Paladin - melee and intense; great damage
Monk - good ranged heals, great single-target; powerful heals; i couldn’t dps for diddy (I don’t PvP or raid and apparently a specific essence was 100% required - so this class got smoked for me) - and was forced to give it up once I got near M15
Druid - easily the most overpowered healer in M+ for going on 6 years. To the point that you best be great if you are a non-druid because you will never measure up. Personally i hate stance shifting and so… my dps sucked.
Priest - honestly I cannot for the life of me understand how they survive in m+ past M10. Heals are just soooo weak.
Shaman - I can actually dps while healing! Score! This is my fav this xpac.
But here is the bottom line truth: healing high keys is mostly a dps thing; meaning they must do mechanics, avoid damage, self heal, self mitigate. They do that and really most healers can function. In lower keys people get annoyed at the healer when they refresh bursting 3 times in a row and everyone dies… of they get 1 shot in fights (newsflash - nobody can heal a 1-shot outside of a miracle pre-BoP).