I can speak from firsthand experience during the magnitude 7.0+ quake here in Anchorage last November. I also work in the telecom industry. Texting worked reliably where voice calls didn't over the cell network because, as Bullwinkle says above, texts are packet based, where voice calls consume a circuit. You can overload a packet based system and stuff just slows down, but goes through okay eventually. When you overload a circuit based system, when you're out of circuits your done until calls terminate and free up circuits.
Not only were virtually all cell sites' voice capacities immediately overloaded with everyone trying to call everyone they knew, but many cell sites were knocked completely offline. Most cell sites (at least here in the Anchorage metro and nearby areas) only have a small UPS system to protect against short-duration drops of AC power, so when those batteries were exhausted they went down. The ones that stayed up were the few that had generator power or were in areas where the power didn't drop for some reason.
As far as service "tiering" (for lack of a better term) for allowing certain calls to go through over others, there is a mechanism in place nationwide that provides priority calling for those involved with critical infrastructure, but as far as I'm aware no cell provider allows you to just pay a fee and buy your way into a higher priority.
I know that everyone's obsessed with their cell phones these days, but there are still absolutely excellent reasons to have an old style land line telephone in your home that doesn't rely on AC power.