The difference is that Kuwait asked for the US to intervene and conquer back their country.
The Iraqis made no such invitation.
No matter how good an idea it might be, it will not happen. Invading Iraq was a very expensive thing to do, but it was entirely optional. Had Al Gore been president, there surely would have been no invasion.
Iraq will not pay the US back. Perhaps some US companies will get cheaper deals on oil, but because of bribery, not reparations.