Law is very much prestige-oriented. UF is still the best law school in the state of FL. Whether or not FSU will catch up, only time will tell.
As some mentioned, FSU may very well place better in government, though just because they do place a higher percentage in government does not mean that UF couldn't do the same. It could just mean that the percentage of FSU grads that want government jobs is higher than the percentage of UF grads that want government jobs. The same comment could go for law firm placement with UF placing a higher percentage than FSU.
As far as Bar passage rate, most people take a Bar Prep class that teaches the materials on the bar. Law school doesn't really teach you enough of what you need to know to pass the bar. If it did, then more 3Ls would forego the Bar Prep class and review their law school materials for the past 3 years. If you disagree with me, talk to some people who recently took the Bar and ask them if they would have been able to pass the bar without having taken the Prep class.
The fact that UF Law is older than FSU obviously means it has more graduates out there. The fact that UF has 400 1Ls each year and FSU has somewhere around 220 means that the gap is getting bigger. The more alums out there, the easier it will be to get a job. When I say this, I am referring to the average graduate. The reality is that the top 10% at both schools will have no problem. Maybe even the top 20%. But everyone else will REALLY be using that alumni network.
Finally, returning to law being prestige-oriented, if you want to take your law degree to another state, the prestige of the school will possibly determine whether or not you even get looked at by recruiters/interviewers. Having a larger alumni network also means that the likelihood that there is an alum in the state where you want to practice is higher.