Note 7 is a great phone, hope you're right and you love it.After seeing the Pixel presentation yesterday, I picked up a Note 7 today.
Not being available through T-Mobile was a huge factor but I'll probably be happier in the long run.
You either have a bad device or something wrong with app or installation. Oculus as example is causing problems (if that is on yours), but an update fixes it. Web view also has causes some problems.
Battery life for me and my medium to heavy use is 4.5 SOT in QHD and over 5.5 SOT in FHD. I leave mine in FHD since see no difference (still looks great) and runs apps cooler including Maps. I only change to QHD for Gear VR.
The only problem with FHD for me is that the AOD is disabled. I use that for night time use next to my bed to check during the night. Wish there was a way to use both FHD and AOD at the same time.