If you've had the car for less than 6 months when you register in FL, you have to pay the diff between sales tax where you bought it and FL tax (6%, as mentioned). If it's been more than 6 months, you don't have to pay the diff. Military or not doesn't matter.
However, if you're a FL resident and active duty, you can move wherever you like and keep the plates, license, etc. They'll put out-of-state address on your license. I think most states will do this for military nowadays.
The easiest way to establish residence in FL is to register to vote. I don't believe there's any minimum time before you can register; you just have to have some sort of local address, and I think a PO Box will suffice. The Escambia County Courthouse is downtown.
To answer the original question, no, I don't think there's any particular advantage to FL vs TX residence, taxes or cars or anything. As you'll no doubt gather from the responses, plenty of sailors change their residence to FL. I've never talked to anyone in the military who was a TX resident and changed to FL...then again, that might just be a pride thing.
