If you are of one of them who wish to unlock your bootloader,root your device you can get sim-unlocked T-Mobile Galaxy Note 3 and use it on AT&T network as T-Mobile variant includes all banss needed for AT&T.
As per FCC documents T-Mobile Note 3 also includes LTE frequencies used by AT&T. Here is the list of bands taken from the back of T-Mobile Note 3 box.
GSM: 850, 900, 1800, 1900
UTMS: Band 1 (2100), Band 2 (1900), Band 4 (1700), Band 5 (850)
LTE: Band 4 (1700), Band 17 (700), Band 1 (2100), Band 2 (1900), Band 5 (850), Band 7 (2600)
You can use below APN setting to get T-Mobile Note 3 working on AT&T neytwork.
NAME: ATT Phone
MMS proxy: proxy.mobile.att.net
MMS port: 80
APN type: default,mms,supl,hipri
Check the video guide below that explains how to get T-Mobile Note 3 working on AT&T.
Source : Xdadevelopers