The main carrier difference would be that Verizon’s CDMA network can’t handle simultaneous voice/data transmission like AT&T’s GSM network can.
The earlier commercials for the iPhone would show something like a guy taking a call, then putting her on speaker while opening an app for dinner reservations, then pulling up a google map, ordering flowers and whatnot all while talking to her. That won’t happen on Verizon, you would have to lose the call, or lose the internet and do one or the other.
Those “can you hear me now?” commercials speak the truth about verizons service. Personally, I can’t stand verizon, everyone I know has verizon but they all have had issues with service at one time or another. I have had AT&T for 8 years and never had any problems at all.
AT&T has better reception in most of NYC, and as @sinscriven mentioned, you won’t be able to use data and voice simultaneously.
I’ve had an iPhone for about 3 years now, I think. I cannot imagine having that capability taken away. You shouldn’t get an iPhone if you’re on Verizon. It’s just wrong, you’re wasting your money and getting less than you should.
Why buy a $6,000 computer if you’re only allowed to play Solitaire?