We had Verizon for many years, but switched to AT&T about a year ago. Mainly because Verizon raised my monthly bill, and were kind of unyielding regarding my higher bill. So I switched.
At least in the Colorado mountains, both companies have spots where one works and the other doesn't. Other than that, I have never had a problem with AT&T not working. Like one poster said, Verizon's claims don't always include data coverage. Plus, both companies coverages don't always live up to their coverage claims.
With the AT&T family plan we are now paying about 50 dollars a phone for data, text, and voice.