There is a single hardware model, but Sprint and Verizon maintain a database of "approved" MEIDs. You can get Verizon to activate a SIM card directly with a postpaid plan, but I've not found a way to get the prepaid Verizon plans on my Sprint iPad Air, even with an unactivated Verizon SIM card.
However, I put in a new T-Mobile SIM into my Sprint iPad, and it worked just as if it was a T-Mobile iPad. The prepaid data options appeared in Settings-Cellular Data-View Account and everything. I would imagine it's the same with AT&T.
Bottom line: Buy either a Verizon or Sprint iPad, based on your own preference. Assuming AT&T works how T-Mobile does on a Verizon/Sprint model, there's no reason to cut yourself out of access to one of the CDMA carriers.