AT&T's argument was that the Verizon ads mislead consumers into thinking the carrier has little to no wireless internet coverage in huge swaths of the country, by putting two 3G coverage maps side by side and obfuscating the fact that AT&T nevertheless does have 2G data coverage in many of those areas. They wanted an injunction that would pull those ads off the air, but the Atlanta judge disagreed.
The carrier says they intend to appeal the ruling, although even if AT&T were to eventually get the courts on their side it's already fairly late in the game, as the ads have already been running for over a month. Verizon had fired back with a rebuttal of its own to the court earlier in the week, which was apparently enough to help sway the favor of the court against the plaintiff.