Sure!
Ah yes, the reason is because I am on a business account with my family/family business on AT&T and they wouldn't allow preorders for phones and any time I'd try it would ask for info I didn't have or for an admin so I just went and bought the T-Mobile variant since it is the same model number and same GSM band support so I figured why not. It didn't ask for any T-Mo credentials or anything. I WOULD have bought the normal Unlocked SIM free version that's Qualcomm but it didn't exist at launch. I hate that they do that as it's the one I wanted. But this was also the first iPhone I've purchased new. I've had 3GS/4/4S/5/5C/6 Plus/6S/SE and all the while only bought them used. I planned on keeping this one longer term since I find that they have matured quite a bit and year to year changes aren't quite as drastic as say the performance difference between 3G and 3GS or 4 and 4S etc and camera improvements aren't quite what they were either.
The T-Mobile and AT&T phones are the same model (A1778, GSM unlocked + TMO/ATT) they all have the Intel XMM 3360 modem where the Verizon, Sprint, and now SIM-free unlocked model have the Qualcomm X12 modem in them (A1660). Yours should say A1784 (Plus variant) on the back.
So they would both have the same modem yes.
It could be both, but I know people complain about T-mo's voice network on the 900 MHz spectrum as being worse for building penetration. But I don't know how much that would affect LTE performance.
As for the Verizon user, I have a friend with the VZW iPhone 7 and his has been fine since launch but they did release an iOS update specifically for them back near launch. iOS 10.0.3 was to fix some of the data drops they were having. So that explains that.
This screenshot is of my 4S and 7 on the same desk same day just a few minutes apart while I reset the 7 and signed back in to things to make it fair. 7 was a fresh restore of 10.3.1 via iTunes and the 4S was freshly reset on iOS 6.1, though they did update the modem many times since then I love the older faster iOS 6 vs something like 9 on the old 4S.
In retrospect I should have put them both into dBm for the screenshots but oh well. I also turned off WiFi and went to load up a couple pages in Safari and the 4S was actually quicker, despite the 7 having some huge number of times faster processing abilities. Haha.