The Illinois game is huge (called the Braggin' Rights game and played in St. Louis every December) but I believe it may have been put on the shelf. Mizzou has won the last 4 or 5 meetings I believe and Illinois wanted to get out of the game (pussies).
But Mizzou's biggest rival is KU. There's as much hate between Mizzou-KU basketball as you see in a Ole Miss-MSU football week.
If you're looking for things to piss off aTm or Mizzou fans... considering that I live in Aggie country and grew up in Missouri, I can help.
For aTm, make fun of their traditions. They have a lot of weird traditions and they do not let them go. The yell leaders is an easy target (youtube yell leaders). You could also ask them the simple question: "If the state of Texas produces so much talent, how come only Texas is good at football?" Prepare yourself for about an hour of excuses.
For Mizzou, just ask them why can't they beat KU in basketball. Mizzou has always been a basketball school, but Gary Pinkel is converting them into a football school. I think Mizzou will fit in well with the SEC eventually, but it's going to be a bumpy start, as they do havee a much more "northern" fan base, as in they wear jerseys and don't know how to tailgate.... but I think they'll adapt quickly.