NO. I was a Verizon customer for 7 years working all over the region they are supposed to be the best - the NE and Mid-Atlantic US. I have just as good service with AT&T, in fact I have MANY areas I get better service with AT&T, and my phone ALWAYS rings. On Verizon, if you are roaming, the chance on your phone ringing is about 30%.
The idea that Verizon has tremendously better service is a myth, perpetuated by lots advertising dollars.
Oh, and let me also let you know that over those 7 years, I referred literally DOZENS of co-workers to Verizon, and was supposed to be compensated by a $50 credit to my account for each referral under a program they had running at the time. I never saw a DIME. So much for better service, too.