UGA is UF's daddy? UGA has only a 9 or 10 game lead (depending on whose count you pick) in a matchup that has been played 100 times, and in the modern era of the sport (post-integration) UF has the upper hand. Even when you include Dooley's dominance in the series in the 70s and 80s. Post-integration, UF is the better program, and especially since 1990 UF is the better program.
I certainly wouldn't say that UGA has no tradition or culture (especially culture; Athens is about as culturally-rich of a little town you'll see). I would say that for a program of its caliber, UGA is kind of lacking in terms of hardware, particularly in terms of national titles and conference titles.
UGA should probably have more hardware than a program like Tennessee, but for whatever reason you don't, and that's with Tennessee being a black hole of suck for the last decade plus.