Re Verizon/ATT/T-mobile (the big 3)
At one time Verizon did indeed have a better coverage map and in places you will find one or the other or the 3rd is the ONLY provider
You might see who T-Mobile has agreements with (used to be AT&T last time I was in the land of no Verizon) But I think it might be Verizon now. or perhaps both These are mutual "Your customers can use our network if no your tower near" agreements. (And ours yours).
But today all the coverage maps are getting to about the same amount of coverage.. Just not allways in the same spot.
T-Mobile is real good on most freeways... But may fail as you move away from them.. But I know places where Verizon is not as well (But T-mobile worked)