UF and Bama are the biggest rivals we have but I think you have hit on something with the ages - a lot of the younger guys (myself included) don't really remember going long stretches without wins onver Bama...a lot of my memories surround a season being spoiled by the Gators.
Having so many Bammers in the area (Southern Middle Tn) and those long stretches in the series makes me loath losing to Bama, Florida has only been a pain in the butt in recent history.
My vote is FL due to the fact I've had to live here for the past three years. Also, we have been trading wins and losses over the past 5-6 years. Bama we have dominated for 9 until last year.