Prices between AT&T and Verizon for text messages payments, plans are pretty much equal.
The voice quality on Verizon is better than AT&T because of CDMA vs. GSM technology.
With Verizon you have the probability that a lot more of your cell to cell calls will be free, simply because there are a LOT more Verizon customers than there are AT&T customers, so your free mobile-to-mobile minutes will be a lot more likely to hit another Verizon mobile, than an AT&T mobile.
Verizon has MUCH better coverage over-all in the U.S. than AT&T, but there are a few, very rare, instances where AT&T may have better coverage.
CDMA (Verizon) penetrates much better inside buildings than GSM (AT&T) does, so you are likely to have a stronger signal inside a building with Verizon than with AT&T, even if you have the same number of "bars" outside a building