First off, sorry about the cut short answers followed by the /ignore. I had too many other things going on. I was hoping you'd take the hint that I was busy. I will give you my full answer here now that I have more time to answer it.
I'm only going to cover Order healers because that's what I know better and that's what the question was about.
I'll start with this. Healing burden is not determined by your group. It's determined by your enemy. You want to build your healing core around what you will be facing if possible.
Again, this is all simply my opinion and is greatly simplified.
The Warrior Priest is an anti-physical, anti-AoE healer. He cleanses Hexes and Curses and is the only healer in game that can cleanse his entire group at once without blowing a morale. He simply does not have the ability to do large single target spike healing unless he puts himself in danger. Choppas hate seeing this healer because he can completely neutralize almost everything he does in a group setting. A Sorceress that relies on Curses like Word of Pain to kill is also annoyed by the WP. The best chance at killing a WP is to use a Witch Elf. Witch Elves can ignore armor. A lot of WPs have tank level armor. She uses Ailments which the WP cannot cleanse. She also does large, single target spike damage which the WP is not well equipped to handle. Other physical damage dealers are not much of a concern to the WP due the ease at which he can stack armor.
The Archmage is an anti-magic, spike healer. Arguably the Archmage has the best single target raw healing in the game. AP is generally not a concern to the healing AM due do all the ways they have to conserve and restore AP. They can cleanse Hexes and Ailments. Due to their light armor and inability to cleanse Curses, Choppas love seeing these on the field. Squig Herders can eat AMs for lunch too with their silence, heal debuff, and heavy physical damage. The AM also cannot cleanse anything a Sorceress does. The AM shares a common issue most players have with High Elves in general. The AM is a very self centered class. It's got a lot of raw healing going for it and a ton of self preservation tools, but as far as offering their group much more than a lot of heals, they don't have much utility.
The Rune Priest is the jack of all trades, buffing healer. He can buff your stats. He can buff your armor. He can buff your resists. He can give you AP. He can buff all incoming healing. He can heal on the run. He can stand still and focus heal. He can AoE heal. And if he had a tube sock, a cardboard tube, a hanger and paper clips, he could probably find a way to heal you with them. He can stack armor to the heavens like the WP or he can have lower armor in favor of better heals. Now obviously, he can't do all this at once. He has to choose what he's going to be good at. He cleanses Curses and Ailments, so he's weak to major debuffing ability of the Blackguard.
So as far as your question, would I rather have an AM or RP? It depends on the situation. I'll take the class with the better player behind it all else being equal. I know it's not what you wanted, but it's the way I see it.