I honestly feel like it depends. Alabama is our biggest rival, so that's the game I want to win the most. However, Florida's 6 game streak over the Vols is pretty hard to stomach right now. Losing both those games really sucks.
I think losing to Kentucky would be awful, but that hasn't happened in my lifetime, so I can't say for sure how bad that will be.
That being said, I'm not sure there's a worse feeling than losing to Auburn. I don't mind if Auburn wins against other teams, but I hate when Tennessee loses to them. Losing to Bama sucks because it's losing to your biggest rival, but losing to Auburn feels like losing to your biggest rival's inbred little sister.