I had a really arrogant T-Mobile manager argue with me that my unlocked AT&T iPhone 5S would not pick up LTE because it wasn't "their" version of the iPhone. When the phone finally popped up with LTE, I shoved it right in his face. He was like its temporary, and you won't get it anywhere else. I laughed and walked out. The point is... T-Mobile reps don't know jack S***.
AT&T and T-Mobile have the EXACT iphone 5S model. Only difference between the two they are both locked to their respective carrier. That's it!