The elitist attitude isn't what people make it out to be. What someone who did not (or could not) go to UF would call elitism, UF alumni would call pride. (And that pride becomes real beneficial when it comes to alumni connections for careers).
"Additionally, since it is so large, having huge class sizes, TAs instead of professors for all classes, and having an impossible time registering for gen ed credits are all concerns."
First, TA's for all classes is a gross exaggeration. As for the rest, that happens at all the large state universities (UF, FSU, USF, USF) unless you enter the honors college.
You can argue the finer points of the two schools until you are blue in the face. At the end of the day, the University of Florida has at least some level of NATIONAL prestige to it while FSU does not. UF has a better reputation to get you into more competitive grad schools (if you go) and greater national mobility.