AFAIK, there are 4 types of Surface 3 LTE models floating around. Each of them have a dedicated SKU (i've seen 3 of the 4)
ATT, Unlocked (non-ATT), Outside of North America, and Verizon (just announced).
What is unclear about these models is whether each of them have different radios supporting specific LTE bands. The surface 3 specification page seems to support all the frequencies (UMTS/HSPA/HSPA+: 850, 900, 1900, 2100 MHz, 4G LTE: 700, 800, 850, 1700, 1800, 1900, 2100, 2600 MHz) however the LTE bands are not listed anywhere.
The only place I've seen the LTE bands listed for the Surface 3 are on ATT model page. (LTE band 2, 4, 17).
Verizon runs on 2, 4, 13
T-mobile runs on 2, 4, 12
So if our unlocked version doesn't support 13 or 12, this might be why you are seeing poor performance on Verizon or T-mobile.
EDIT: I found out the modem is the Intel 7260 Modem, which theoretically supports all the US bands and most Global bands.