In dungeon its position, then player importance, if group take heavy damage healer is kind of busy, group is doing fine but some messed up boss mechanic healer rez.In a dungeon I think it's just whoever is best placed to do so. A few seconds of not tanking/healing in a dungeon shouldn't cause a wipe in most circumstances.
In a trial it's got to be DPS.
Yea this is what I was about say in trials off tanks should res if one person diesActually, the Off-tank should rez if he isn't needed at that particular moment in the fight. If he is busy, then its the DPS. It all depends on the fight, but the main tank and healers should never have to rez.