From what I recall in having attended Vol tailgates and games for 10+ years...
Georgia fans were the worst.
South Carolina fans were, by far, the best.
Vol fans are pretty cool UNLESS you mention Texas. They are somehow absolutely obsessed with the "real UT" thing. Which is weird, because I never, not once, thought about them until I moved to Knoxville.
Kentucky football fans - kind of cool. KY basketball fans, not so much.
Florida fans were pretty cool if only for the fact that they drove my Vol friends crazy. I was up there when the Gators beat TN just about every year.
I don't recall much about the MIssissippi teams. I'll give them a pass due to Kiffin and Leach.
I'm not sure I ever met a Vandy fan. That's Nate Bargatze's school/team, so they're cool in my book.
Arky fans were terrible. You know it's bad when Vol fans are making fun of the "hillbillies".
Almost forgot. Aggy did play there before they joined the SEC. It was funny because I warned my Vol friends about them, and they didn't disappoint. Effing idiots walking up and down The Strip, wearing those stupid ass overalls, yelling and whooping. My friends were all, "Ok, we'll root for the Longhorns after this."