There is no contest to me, Verizon all the way.
I am an IT Manager for my employer and am responsible for all telecommunications. I have 30 lines with AT&T and 10 with Verizon.
I regret that many of you have had a poor customer service experience with Verizon, but my experience with Verizon customer service has been top-notch. Their people, in general, have been friendlier, more professional, and effective. I work with either customer service or my rep. AT&T, on the other hand, keeps changing where I get my customer service from - now I have a small business group number I call, but it sucks just as much as any of my other contact points with AT&T I've had. Their people are uneducated about their services, products, and procedures - many times, I tell them how to do what they need to do (change such and such features on the line, transfer me to whatever department, etc.). They are also generally less-friendly, less competent, and less motivated on reaching a resolution for my problems. I am FREQUENTLY told whenever there is a problem with something, I have to wait up to 10 business days for support ticket resolution - sometimes I'm lucky and call back, reach somebody with an IQ over 80, and my issue ends up resolved, sometimes not. And I'm talking simple stuff, like ordering iPhones!
On the technical side, its not even close. No company is perfect everywhere, but Verizon has consistently reliable connection and data speeds in far more areas for myself and the traveling sales staff I support. Even in Fresno, a reasonably large metro area with nearly 1 million people, I have shoddy 3G coverage - and even with 5 bars of consistent 3G, I commonly have "dial-up" speeds from their lack of bandwidth. EDGE is virtually useless as even a lower-grade data alternative. AT&T's only advantage is that they can do data and voice simultaneous in 3G areas, but it is too much of a price to pay.
AT&T's oversensitivity to this current ad war is ridiculously telling as well; they are like a kid caught with their hand in the cookie jar, saying the devil made them do it. Frankly, T-Mobile would be better for the iPhone at this point.