(Former Gator here as well)
Funny, b/c I agree with you about it being FSU, but I'm also an late Gen X'er. If you were to ask them earlier GenX'ers folks, they would claim it to be Miami.
Apparently prior to 1977, FSU was like TXST; the laughable loser to Florida and similar to UT / TXST of today, they were not perceived to be equals. Once Bobby Bowden started winning consistently in the 80s/90s is when that rivalry amped up and the tides changed.
Since the University of Florida is the Texas Longhorns of Florida, what's it like to live on both sides of the street?
Have to say that yes the arrogance and perceived prestige of being a Gator is on par with UT's arrogance here in Texas.
Funny thing is that when I attended Florida, I hated Garnet & Gold... but now that I am a TXST Sicko, I want TXST to emulate FSU by following the path they took; i.e. beating team bully teams on the field or court to earn that respect and change the perception. I know that it will take decades to see TXST/UT being spoken about like FSU/UF is now; but I'd love to see it happen before I pass.
However shifting gears a bit, the state of Florida from what I know didn't or currently doesn't have a Permanent University Fund like barrier of entry for other in-state schools. Therefore the rise of FSU in popularity in the 80s/90s didn't have our unique State Funding disparity issue to grow the brand. That is likely why more recently UCF, South Florida, and to a lesser extend FAU have seen a increase in popularity (excluded FIU - because like UTSA - its a glorified community college).
Another obstacle to it all (besides unequal state funding allocation and decades of student apathy ), boils down to TV exposure. The top tier brand schools have been on over the air TV / cable / prime channels and local sports news outlets for decades. As a Gen Xer, I grew up easily influenced by what was on television, and my influential years were during the Steve Spurrier days and eventually solidified when I got accepted to Florida. I still hear stuff from other Sickos today that they still root UT/A&M because they grew up watching the rivalry and picked a side. For me it wasn't until after graduating that the Cats won me over. It was that 2005 GaSo Playoff game that still to this day is the best football game experience in my lifetime. It was then when I was provided a glimpse of the potential that TXST could muster up (dare I say - the sleeping giant). Nowadays - I do whatever I can to promote the TXST brand and root for the underdogs in college athletics, with the intent that one day TXST will be perceived to be on an equal level as those other brands.