Ok... if this is not an occupation then it is really no contest.
This would have to be a scenario where the US did not care about the world's opinion, as they would leave Iran in an absolute mess, possibly shooting themselves in the foot.
Ground forces would probably not get involved, or if they did, they would be strikes with overwhelming force without regard to civilian casualties (again, they don't care about world opinion). Much of Iranian infrastructure would be decimated.
The attack would be over relatively quickly, With most Iranian forces going into hiding or surrendering (shock and awe and all), and the government officials dead, captured, or also in hiding. US Military casualties would be light, Iranian civilian casualties in my scenario would be fairly high. Our navy is not called the best in the world for nothing, so i would say our navy casualties would be from light to non-existant. Air force losses would also be light to non-existant. Once we left, Iran would fall further into chaos, possibly giving rise to a government that could require more intervention. At the same time, there would be much outcry against US tactics, aggression, and not staying to rebuild Iran.
All the loons above me state the war is still going on in Iraq when it has been over for years. We are currently occupying Iraq and together with their government fighting insurgents you dildos.