I used the T-Mobile Note 3 for a while. I unlocked it using Chanfire's app. When using my AT&T sim card in it, I found the LTE to be horrible, despite supporting band 17 (700mhz) In places where I had average LTE on the iPhone, the TMO N3 would be on H+ or have the worst LTE signal. This was frustrating. I took it back. It was fun to flash roms and kernels though.
I got an awesome deal on a new AT&T note 3 where I couldn't pass it up haha. At first I noticed my AT&T LTE signal was not as good as it should be. I then created a thread about it. I cleared the cache in my phone and did a full factory reset. Now my LTE seems fine. Constantly sitting on -93db on my desk where my iPhone gets the same.
I'm pretty happy now with my AT&T Note 3. Rooting was so easy and gives me everything a custom rom would.