One major difference between the war in Vietnam and the more recent wars in Iraq is the quality of equipment. During Vietnam, our enemy was the USSR in the form of Charlie. We were fighting an army equipped with weapons very much comparable to our own, if not better. As an example, the AK47 was far and away a much better suited weapon than the poorly designed M16A1.
Furthermore, the terrain in both scenarios played a very significant role in their outcomes. In Vietnam, we were trying to establish air superiority and were still relying on tactics that had been effective in World War II. Think here of Operation Linebacker. It was our position that we could simply carpet bomb the Vietnamese into submission. Unfortunately there weren't any real targets of opportunity. There were no centralized production facilities, no major industry that needed to be shut down. As stated earlier, the Vietnamese were being supplied by the Soviets, so carpet bombing wasn't the answer (unless of course that bombing had been directed at Soviet resources, but that's a whole different can of worms).
Now take a look at the Iraqi terrain. Wide open desert and a self-contained infrastructure. This leads to the perfect use of the type of tactics we attempted in Vietnam. However, technology has progressed and there is no longer the need to carpet bomb. We can use satellite guided weapons to accurately pinpoint and destroy targets. Cruise missiles with ground following systems can fly hundreds of miles and hit a particular point in a castle. We can surgically remove the enemy's capability to make war.
Our ability to own the skies, and grind the war-making machine to a halt very quickly de-moralizes a fighting force. The Iraqis are now fighting with sub-standard equipment against an enemy that owns their skies, has destroyed their ability to continue to wage war and has them surrounded.
If we assume that the Iraqis were indeed an effective fighting force, how would we have fared? Our strategy would have been the same: destroy their ability to wage war. A fighting force can be the most effective force in the world, however if they cannot wage war they are rendered useless. Our casualties would have been considerably greater than they were due to the more effective fighting abilities of the Iraqis; however, the outcome would have eventually been the same simply because we could outlast them.