We have both Verizon and AT&T.
We found AT&T had better 4G or LTE coveage up the east coast and in New England last year. We found Verizon was limited to 3G most places.
In Arkansas, Louisiana and Texas this year, we've had great Verizon LTE and 4G coverage, and consistently good AT&T coverage.
There are places, and sometimes there is no understanding why, that one will not work or work very poorly, and the other will work.
We have also found that once you get west of I-35, you start hitting areas where there is no cell phone coverage of any kinds, or if there is cell coverage, there is no data coverage available.