I think its possible for either to win one. LSU fans seem to forget that spell of years where they sucked. They were just a average team. I wanna say it was from around 1986 to 2001. The best bowl game they had during those years was like the Gator Bowl or something. Saban came along and changed the program.
USCe was also in a stretch of tough years. From 1990 to 1998 they had only three winning seasons. Holtz/Spurrier came along and built them into what they are now. All the while they are in a relatively small state with another major college in Clemson.
The point is it can happen at either of the schools. I'd say if I had to choose Ole Miss just because for whatever reason traditionally its been the easier school to get top talent to. (The talent from the female side is 2nd to none)