AT&T Will Pay Me
Approximately zero percent of the population seems to understand what AT&T is trying to say with its bizarre ad campaign about how "I need a phone that works where I live, a place called Bizarreportmanteauplacename," probably because the ads are really dumb. What they mean, for the record, is that AT&T's phones operate on the GSM standard which is much more widely used outside the US. Thus, an AT&T phone will (for an appropriate fee) work pretty much wherever you want to go. A Verizon phone, by contrast, will not.
Given that most Americans don't do much international travel, this probably isn't a compelling consideration for all that many people, but if you do go abroad regularly it's a big difference.