I guess dps is the less gear dependant, with healers being the most.
Tanks become pretty easy to keep alive once they reach some caps in stats, and they get there pretty quickly. Past that, they just become easier and easier to heal until it gets plain boring. That's assuming a decent gameplay of course, no matter the gear a bad tank will die.
DPS see a very sharp increase moving from blue to purple, but it quickly flattens. For example on my hunter I didn't really gear up since T11, yet I get pretty similar dps than near to full T12 people, only Arcane mages really put a decent slap at my face.
Healers on the other hand are terribly gear dependant. Sure you can get a high HPS quickly, but you'll run out of mana just as fast if your gear isn't on a par with the content. On my full T12 pally FL encounters are plain easy, on the half T11 priest, I gotta keep a close look on what I do to get to the end without going OOM.
Sure tanks/healers/dps do better with better gear, but healers have it way harder if their gear is inferior.