While i can see both sides of the argument, i'm personally leaning towards a "mixed" xp system. I think that a pure objective based xp system limits the joy of exploration.
The example i'm thinking is this: You get a quest to go to area "X" and clear a crypt of skeletons. An objective based system would work perfectly here. You go to the area, you enter the crypt, you kill the skeletons and earn the xp on completion.
But what about the rest of the area outside? If i decide to explore all the map and bump into random encounters, a bandit group or a group of orcs, what is the point of it if i dont get anything at all? They might not even drop any weapons or gold, so why did i have to go around and explore the map and do combat?
I think that xp should be rewarded on kills as well but it shouldn't make a big difference as in, the player that did only the crypt objective should not leave the area a level lower than the one that killed everything.
Edit: Unless they manage to add automatic objectives on all the encounters and situations in the game, which i think is pointless and too much meaningless work