Verizon has far superior voice quality and call reliability than AT&T.
This is relative based on location. I'm a former Verizon subscriber for personal use and I continue to have a business phone with Verizon that I carry along with my iPhone so I always have a side by side comparison. At my house and at my office, Verizon reception and voice quality stinks - AT&T's is much better. I made a trip to West Texas to visit a friend at his ranch not long ago and during the drive there and back, I completely lost reception with Verizon at several locations but not once with AT&T. I didn't have reception with Verizon while at the ranch but I did with AT&T so again, this is relative.
I can direct you to some websites where some existing and former Verizon subscribers are singing the same tune as you about Verizon - crappy customer service and support, etc. which is also relative.
I've had one major complaint with Verizon's customer service since the summer of 2001 which I won't get into here, but since becoming an AT&T subscriber 3-4 months prior to the iPhone's release date, the few times I've contacted AT&T customer or technical support, my experience was excellent with no complaints.