How the phone is going to perform depends on your AT&T coverage. As far as receiver sensitivity, the Note 3 is good. (I'm sitting at -105dbm at the moment, with no problems. I've had calls with -120dbm with no problems also.)
But if where you need coverage, AT&T doesn't have signal, the phone won't work for you.
(The Sprint version is also a good phone - but Sprint's signal in my daughter's home runs from not measurable to non--existent. It's fine in her back yard, on the front lawn - but the house is in a knife shadow from a ridge between the house and Sprint's tower. So a Note 3 would be useless to me if I used Sprint.)
There are very few phones made today that have bad receivers (other than defective phones) and the transmitters all put out the maximum allowed power. Comments like "I have a Note 3 on AT&T and the reception sucks, so the Note 3 is a terrible phone" are useless without the signal strength. Tell me that you're getting terrible reception with a -85dbm signal and I'll agree that you have a terrible phone. But if there's no signal, or a marginal one, no phone (with the exception of one old Samsung candy bar from about 10 years ago, or the old Motorola 7868) will get good reception. It's like claiming that your car gets terrible gas mileage, but neglecting to mention that you only use it on the beach in soft sand.
Rule #1 in getting a cellphone - determine which carrier has the best signal in places you need signal. I donb't care what fabulous offer Company X has, how cheap the phone is - if they don't have a signal at your house, the phone and the carrier are useless to you when you're at home.