All things being equal and available...fresh (not frozen) cut mooneye for channel cat, live bullheads and chubs for flathead. Big channel cat prefer live or fresh cut bait--save the liver, stink bait, ivory soap, and all that for the eating size channel cats.
Live suckers, wild or from the baitshop, will catch flathead and big channels if you can't get bullheads or chubs. I have never had much luck for channels or flats with cut sucker. Fresh smashed chubs, on the other hand, work alright for me.
I prefer catching my own live bait, including creek chubs, bullheads, and suckers. It's a little more work, but wild bait is usually tougher and works better if you take proper care of it.
If you are a Wisconsin resident, and hold a Wisconsin license, I *think* you may have a few more live bait options for the Mississippi than we Minnesota residents do. Check Wisconsin's regulations to be sure if this is the case.
If Wisconsin residents can use live
sunfish as bait, they work well, too. In Iowa it is legal to use live
sunfish, and I have had good results with small green
sunfish and bluegills.