I have Verizon.
I've never had any problems with voice connections on base. But even with a very strong signal strength, I've had consistently lousy LTE data speeds on base for a few years. I'm used to waiting several seconds until data starts flowing, and even then it is far too slow for video or downloads.
The southeast corner has always been the worst for me, but all across base is pretty slow. If I really want to get something done on my cell, I switch off LTE and use the 3G connection instead - it's a lot faster. But that workaround won't work forever - Verizon is phasing out the 3G system entirely.
The problem comes from the fundamental cell system design; towers have sets of directional-capable antennae that can be "beam steered" to maximize signal strength in a certain direction. (That's why they often have a triangular set of 9 antennae pointing in three directions.) We have 10,000 people on base who all are desperately trying to bypass the equally horrid NMCI system. So the few cell towers in the vicinity of the base are all overloaded by shoveling vast amounts of data through the fixed number of LTE connections that can be beam-steered in the direction of the crowded base.
You'll find the same thing happen anytime you go to an event with a huge crowd (NFL game, or big outdoor concert). Put tens of thousands of people in a very small geographical area, and the LTE speeds for everybody will drop like a rock, sometimes to "just can't get any data" levels. There just are not enough channels available for that many signals.
The only thing to fix it would be more cell towers. I just saw a new tower going up near the Hermanville/235 intersection - I'm hopeful that will help.
