I would go with Verizon. Verizon's 4G network is far more superior than AT&T with wider coverage, although reports say that AT&T's 4G LTE is faster than Verizon. That may be due to people not adopting LTE as much on AT&T than Verizon yet. In my opinion, the 4G speeds don't really matter as long as they deliver high speeds. About 10mbps + is satisfying enough for me. I don't see the point of higher speeds on a phone , although its good to have.
But hey, don't forget that although 4G might be available, there are many times you would fallback to 3G or even 2G speeds. In this case, Verizon still wins as although AT&T still has better speed in some cases, Verizon's 3G is known to be reliable. Yes, they may not typically get speeds above 3mbps, but they do get decent speeds of about 1-2 mbps most of the time (for me). In extreme cases, of course, below 1mbps . AT&T on the other hand, experiences high speeds sometimes but is mediocre. You could get high speeds but you could also get extremely low speeds. (Again, hearsay!)
Also, AT&T is known for dropping calls since the iPhone came out. Verizon, on the other hand, is a reliable carrier with much lesser dropped calls. However, I'm sure that I've also heard that the situation at AT&T has improved and this can't be ignored.
In terms of pricing, they are actually both equally expensive. But I heard Verizon has better value for its data plans. (Not sure for this actually, need to check my sources again) .