Alligators do not have great digestive systems, they prefer well rotted meat. Sometimes they will put a fresh kill under a log and let it rot for a week or so before eating. I used to hunt gators and have taken a few just after they ate such a meal, its not hard to tell! Fortunately the stench doesn't effect the gator's meat, just the gator hunter having to handle it...
Baiting gators is done with very well rotted meat, usually chicken or beef lung left in a cooler in the sun for a few days (no ice) makes the best bait. Be grateful those gator hunting shows you see on TV don't have smellavision...