I'd say 01 Miami was the more complete team, but the gap between them and 04 USC is not that big.
I think people don't remember how many good players USC had on that team, and are also judging them based on how their NFL careers have panned out - which is silly to me.
USC had 23 players on the 04 roster that were drafted in the 1st 3 rounds of the NFL draft. That includes a 1st round QB, a 1st round running back, a 2nd round running back, 2 2nd round WRs, a 2nd round TE, 2nd round LB, and most of the offensive line. They had a ton of good players.
LenDale White, Reggie Bush, Matt Leinart, Fred Davis, Dominique Byrd, Darnell Bing, Dwayne Jarrett, Steve Smith, Ryan Kalil, Winston Justice, Sam Baker, Sedrick Ellis, Frostee Rucker, Lawrence Jackson, Dallas Sartz, Keith Rivers, Lofa Tatupa and Terrell Thomas.
Not to mention USC absolutely destroyed Oklahoma in the NC game. And Oklahoma was much better than the Nebraska team that Miami beat.
All that said, again, Miami was much more complete as they were hands down better on defense and special teams, which is why'd I'd give them the nod over USC.
I think the offenses are comparable, I'd maybe give a slight edge to USC there, but Miami was hands down better on D and SPT.