I have lived in the west for 8 years now, and traveled pretty extensively and have had Verizon and AT&T and noticed not much difference in the past few years between the two. Sure there are places that Verizon works better, and then there are places (like in the Sawtooth range) where AT&T works best.
When I first moved to Moab, Verizon was the only one to consider, five years later, AT&T was just as strong and in fact, they were the first to bring LTE into the Moab area. I also traveled quite a bit to the outskirts of Ouray (off-road purposes) and had friends with AT&T who could surf the net on their smart phone and I could not make a call with my Verizon smart phone.
One time in the back country of Capital Reef, it was reversed; we who had Verizon could surf, those with AT&T had smoke signals.
Just a few weeks ago, I basically traveled from Reno back to ID and talked to a few people the entire way. I will say it was using my Onstar on my 2015 Silverado, but I was warned by many that AT&T would not work in the middle of NV; well, it is true that AT&T hasn't as many antennas as needed, but they use 3rd party vendors and the service and signal was just as good. No extra charge for using a 3rd party, and really would never know you were using another carrier if you didn't look at their maps.
All I can say is it worked great for me. (Admittedly, onstar is a lot more powerful and has a larger antenna, sitting high outside the truck.) And a good friend lives in Winnemucka NV and he has AT&T and always answer when I call!
I believe it is a crap shoot between the two; just knowing in some areas one will work, one won't. That is something I would not have said five years ago.
Best thing to do is compare their coverage maps. And make sure to check 3G as well as 4G coverages. I have found that in some areas one of the carriers will offer 3G where the other carrier offers nothing. And 3G is better than 0G. Also, consider that both companies (probably the others too) are not totally accurate.
When I first moved to Moab, Verizon showed coverage on I-70 between Grand Junction and Green River...well Verizon dropped out about 10 miles inside the UT border and did not pick up service until Thompson; now, since Verizon added a new tower at Danish Flats, you pretty much have service the entire way on I-70.
However I'll also say from experience; Verizons map showing coverage in the San Rafael swell area (north/south of I-70 west of Green River UT) is BS. I have camped there enough to know I had no coverage on my smart phone or via Onstar on my 2013 Silverado. Can't speak for AT&T but I'll try that out in a few weeks.
I will say if Verizon had not continued to up their rates I probably would have remained with them; but when my contract was up; AT&T was the cheapest for me, and on top of that, the phone was 100 bucks less. And I have not been sorry for the change