Just going by this thread... Maybe I'm lucky with my PC version, but it looks like the 360 version is more prone to bugs/freezes. I've had a couple random crashes, which I think may be a deal with having a lot of speed gear on my assassin I just recently made (seems like sometimes I run by so fast that it screws up with gossip? not sure really, it just seems like it only happens with guards), but never the extent of the freezes/crashes that seem to get mentioned in this thread by most of the 360 players.
Anyway... great game. I'm not sure if I'll ever finish Oblivion (well, finish as in beat the main quest), but I'm really loving it. It's almost going to be like, my modern day Fallout 2 - that is, an RPG that I'll replay a bunch with completely different character types (good, evil, various specializations). It's almost a shame this game came out so early, cause now most other games are going to disappoint on some level! But wow, I'm really impressed at what Bethesda's done. This is the best RPG I've played since Planescape: Torment.