I have both Verizon and ATT and Verizon is far better service. If my Verizon cell works then the MiFi almost always works as well.
Don't depend on the coverage maps for any carrier unless it says no coverage! They are largely marketing hype that is out of touch with reality - with reality being a cell phone doesn't work. I have an outside antenna on the roof (12' high) and Wilson amplifier that helps to extend my coverage which is then closer to the coverage map. But it wasn't cheap and the LTE coverage equipment is even more costly.
Also be careful with phone capability. ATT decided my iPhone was 4G because they found a marketing hole and made a software update - everyone knows that the equipment is different! It is NOT LTE. Verizon says they will have LTE coverage for their entire network by the end of the year - ie installed in every tower.