Network: Verizon was certainly the best. However, AT&T is not much far behind. The complaints have been exaggerated because ATT is the only one that offered the iPhone (which, until recently, was the only one that could offer the kind of services ATT was getting hammered about). TMobile, unfortunately, is just really bad.

Customer Service: Verizon sucks. Stay as far away from their customer service as possible. AT&T is fantastic, once you realize that the stores are terrible. Their over the phone customer service has been amazing. Their representatives have, under several occasions, removed fees, and charges, or moved me to a more suitable, but cheaper plan, without any prompting. However, TMobile edges ATT slightly, because their customer service is more consistently good across the spectrum (including stores).

Openness: My Verizon phones are a locked down mess. And being CDMA means you cant use your phone anywhere else. My unlocked iPhone, was usable all over the world, by simply inserting a prepaid local sim-card. Even better, when I have friends and family visit, I can get them a sim card as part of my family plan ($10/month and $15 for the card, which they invariable waive off), and use it with their existing phones. TMobile shares the same advantage, but is slightly better because they are far less hesitant to unlock your phone.

TMobile would be my favorite network, but unfortunately, their coverage is simply too poor. Since ATT is only slightly behind TMObile in customer service, and openness, and far ahead in network quality, I think they are easily the best among the 3.