We have ATT phones, and a Verizon MiFi hot stop for internet.
Right now we are sitting at a Corps of Engineers CG 20 miles northeast of Dallas. We have great connection through the ATT phones - but the Verizon MiFi cannot connect. Neighbor in the next campsite is complaining about not being able to make a phone call with Verizon.
Every network had dead spots and places. In Ruidoso, NM last August - ATT was poor 3G - would barely load weather radar in 5 minutes. Verizon was perfect.
There are some very big areas in this country that neither network covers. Heck, probably 20-25% of the land area of Texas has no cell phone coverage. We've camp hosted at a national park and a state park - and neither had any cell service. For one it was a 30 mile drive to cell service - the other it was 6 miles.
We were planning to go with Verizon for the cell phones, but after traveling a bit - we feel that Verizon for a data plan and keeping ATT for phones is the best answer. (Also 20 gb per month with ATT for us than 10 gb with Verizon.)