If you live\work\travel in good AT&T areas, they're 1000x better. The technology is better, the network deployment is better in most areas, and the functionality of the phone is as Apple intended. To take a smartphone with all the bells and whistles and not be able to be on a call and send off a text (or iMessage), or check directions, or do anything requiring internet, is plain primitive.
I would sooner go T-Mobile and live on EDGE before I'd go Verizon, because at least then the crippled phone would be saving me money. Verizon has done a fantastic job in marketing the last 10 years. They've got people convinced that their network is better. Don't get me wrong, in some places (particularly more rural, non-densly populated areas) it can be better, but that's where they have focused their effort. In a way it's smart because they know they're never going to beat a CDMA carrier, so they have to focus their efforts on the tier 2 markets. Look at their LTE map and you'll see what I mean. How do you think they can say "we have 20x more LTE than AT&T" ... because they light up cities like Boise, Bozeman, Billings, which require 1/20th of the manpower and resources to do. That's where their loyalists come in.
If you live in a top 200 city, AT&T has always and will always be your best network option for a fully functioning phone. All carriers have dead spots, so it comes down to where you live\work\play, and each has to make their own decision. I would not personally go with VZW though, as that no simultaneous voice and data would be going back into the stone age.
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Sorry, for those of us with iPhones, "text" is now a commonly used word for "iMessage" ... on Verizon you cannot do that. Nothing that uses data while on the phone.