mesmers also don't have much AoE capability, if you really enjoy AoE you should keep that in mind.
Standard shatter build and a hybrid sword-offhand/greatsword build both provide considerable burst. In fact, a properly built shatter mesmer can dish out well over 20k damage in a matter of mere seconds. On top of this, both builds also have decent AoE capability (thanks to both Shatter and most attacks hitting at least in cone if not in AoE), though nowhere near what an elementalist can throw out.
To OP: It's hard to compare them up-front, especially without specific builds. Generally, Elementalist is squishier (even compared to glass cannon mesmer) and has more AoE (by more AoE I mean they're completely unmatched when it comes to attacking structures and one of the best overall AoE professions in game, period), while Mesmer has a ton of different utility tools and abilities of dual nature (both attacking the enemy and supporting himself/his allies at the same time).
Which is better? None. Both. Depends on the situation.