The NT34 is a smaller boat than the AT34. Narrower, shorter, lighter. The NT34 used to be called a 32, the AT34 is now called a 36. The AT34 is a little closer to the NT37 (now called a 39), although again, the NT37 is bigger than the AT34. They don't really match in sizes. I own an AT34, looked at NT34 before that, if I switch it might be to an NT37. I've talked to many owners of all of these boats, including some that have switched. Differences in economy aren't huge, with the nod going slightly to the NT as they are narrower.
One thing that annoyed me on the NT34 is the hatch over the rear saloon door, required because of the steps up to the cockpit. You have to open the hatch to open the door, and I go in and out that door all the time. On the AT34 and NT37, it's just a door.