Verizon service is better, but I like the One X a lot more than the GN. Tough choice.
AT&T is always going to have a better selection of phones than Verizon because it is GSM.
For example, AT&T has the following Verizon doesn't have:
1) HTC One X
2) Samsung Galaxy Note
3) All good Windows Phones
4) 100% open GSM Galaxy Nexus (no blocking of Google Wallet)
5) Samsung Galaxy S II
and the possibility to import phones from Rogers/Telus which may have a different selection but still being 100% compatibile with AT&T's LTE network.
The only advantage Verizon has is Motorola phones, but the Droid RAZR is 6 months old and STILL doesn't have ICS.
What about T-Mobile? The only thing that has me tied to VZW is unlimited data, otherwise I would jump on the GSM bandwagon for the better phone selection.
I have the Galaxy Nexus on Verizon and am generally happy. The Nexus device was wrought with problems in reception and screen problems, but I think they are getting ironed out. I had to go through 3 devices to get one that worked well. There are tons of folks out there with Nexus issues. It is not that it is a bad phone, in fact, I think it is one of the best out there but it had a troubled start...
Also, Verizon is one of the only carriers to not allow unlimited mobile to mobile regardless of carrier. They only allow unlimited Verizon mobile to Verizon mobile with a 10 number-per-account list of those you wish to be unlimited. Otherwise, their phone and mobile data networks are top notch.