I currently have a tablet on VZW and a couple of phones on AT&T. I have to say that I like AT&T better than Verizon Wireless. There's only one place that I go that I have data coverage with VZW and I don't have it with AT&T; that is deep inside of my church's basement. Other than that, I have good coverage in the Maryland suburbs of Washington, DC. In all other places, my data on AT&T's LTE network is much faster than my data on VZW's network. I prefer AT&T's customer service over VZW's. Verizon Wireless service reps are as sweet as pie but only as helpful as pie, as well. AT&T's reps are usually nice enough and can resolve most issues that I call in about.
The two areas that have shown consistent problems were getting unlock codes for phones and new changes in policies and the rep training related to those changes. If you're on this forum, you may be the type of person that wants things as soon as AT&T makes them available. This is a problem many times, because the change and how to do it may not have made it to all reps on the first day. This has sometimes been related to unlocking phones; if AT&T changes a policy and you can get your phone unlocked today whereas you couldn't yesterday, be prepared to wait a couple more weeks so that everyone will be trained on how to do this. The other issue has been that they call phones exclusive that are not exclusive, such as the Samsung Galaxy S III. AT&T doesn't unlock exclusive phones for at least six months.
In the overall scheme of things, the above have not been major issues, and I prefer AT&T. The biggest reason that I can say that is because most times that I've called AT&T have been for issues/questions that I had or caused. However, all of my calls to Verizon Wireless' customer service have been for issues that they created in the first place.
As for phones, the Nexus 4 is a great device. Keep in mind that you will not have access to AT&T's LTE network unless you make some modifications to the device. I have heard that these changes are illegal, but I doubt that the FCC will come knocking at your door for these.