What conference really considers FSU a prize? The only conference that wants FSU other than the ACC is the Big12. Florida would block them in the SEC/SEC doesn't need them to increase market, they're too academically inferior for the B1G, and too far for the PAC.
FSU will definitely recruit better. They get to increase their profile playing up to 4 Texas schools. Go to their roster profile on ESPN and see that they have exactly 3 players from Texas. The vast majority of their team is from the state of Florida with Georgia being second. If FSU was recruiting really well, they'd have a more nationally diverse team.
The Big 12 is the realistic alternative for FSU, but they're by far the Big 12's best option. Do you really think that the Big 12 will fill up on other schools not named FSU? FSU will get taken care of. They don't have to worry about schools "stealing" their spots (and honestly, who is going to go Big 12 if FSU doesn't). That allows FSU to be very patient.
As for recruiting, most schools recruit local. That's no suprise. But your kidding yourself if you think FSU is not doing well. According to ESPN rankings, their 2012 class was #2 in the nation (behind Alabama). 2011 was #1 overall. 2010 was #6. 2009 was #8. They're doing just fine. The idea they're going to get this windfall of Texas recruits by playing one (maybe 2) games a year there seems misguided.