From my daughter's materials I see that the SAT score difference is nearly 100 points, isn't it? That's pretty big. And UF has a much bigger pool of students at the top (national merit scholars), which gives it more national prestige. I think that there are major differences in national reputation. For example, UF is an AAU member with a university president with a national reputation. FSU has a former football player and state politician hardly known outside of Tallahassee as president. Look at US News and NRC reputation rankings based on reputation score. UF does substantially better in almost every program than FSU. Also, visit their web sites. UF promotes itself as a serious research university. FSU promotes itself as a sports school in a state capitol that has some research. I see a big difference, to the extent you might be buying the prestige of the university, which should be a factor in deciding where to go to school. Perhaps I am introducing some privincial bias. But I did attend FSU and I am from S. Florida. UF is clearly the top choice for most of the top HS students in S. Florida. Most of my daughter's HS classmates are going to FSU becuase they did not get into UF. Everyone she knows who got into UF is going -- save a few mmusic types and some misguided kids with parents who are FSU boosters. Unfortunately, at present FSU is seen as the party school alternative to UF, for those who did not get in. The law schools are much more even, but there is no real competition between the universities if we are talking about undergraduate or graduate programs more generally -- UF beats FSU in almost every area (music and performing arts the exception).
FSU isn't considered an overall weak university. Their average incoming GPA for college freshmen is a 3.8. UF's is a 3.9. The SAT/ACT scores are almost the same(Uf has a very slight edge). Speaking as someone who works in graduate admissions in FL,I can say that FL ad-coms consider these two schools to be the strongest in the state.However,that's FL. The rest of the nation,except for maybe parts of the SE,doesn't give a damn about either school.Neither of them will help you get a job in NY. You're better off going to a 4th tier in NYC. Neither school has any pull outside the SE.
The one area where I think it will still take quite a bit of time for FSU to catch UF is in its alumni network. Rankings may flip-flop, but I think it will take more than 5 more years for the good ole boy network of the south to be affected by the change, IMHO.