Indeed, it is possible to contrast the fighting in a number of ways. One way is the general direction we are trying to fight. In Vietnam, we hoped our units could fight big-unit battles on the borders of South Vietnam in the hope that this would keep North Vietnam from invading and allow the South Vietnamese to pacify the Viet Cong. Despite the fact that the communists required supply lines to maintain their forces and despite our major effort, we were unable to seriously impede the flow of supplies and men heading south. Sure, we increased the cost to Hanoi to move men and material but they had superpower backing, too.
In Iraq, it is pretty much the reverse. Given the much lower supply needs of the enemy in Iraq and the plentiful munitions and money inside Iraq already, it would have made no sense to seal the border as a first priority. There are no regiments and divisions of the enemy that are trying to take over Iraqi territory. We don't even see platoon-level attacks any more. I already noted that protecting the border was probably irrelevant to cutting off the Baathists and jihadis from arms. So guarding the borders wasn't necessarily the best strategy. In addition, in Vietnam the South Vietnamese troops and government weren't that effective in the beginning and so failed to pacify the interior. Had we tried to rely on the green Iraqi troops we created to secure the cities while we put a dense defensive line along the Iraqi border, the Iraqis would not have ground down the enemy and we would have been wasting our time and strength stopping very little coming in.
Look at how Strategypage describes what is going on:
The battles in the Sunni Arab towns around Baghdad, and in western Iraq, continue to grow. The fighting is triggered by Iraqi police and troops moving into Sunni Arab towns. The local Sunni Arab gangs have to either fight, or submit to police searches. These lead to confiscation of weapons, munitions, money and military equipment, and the arrest of those involved in terrorism or other criminal activity. The police training system, built up over the past two years, is turning out thousands of police, and commanders, each month. These are sent right off, along with the growing number of Iraqi troops, to the rebellious Sunni Arab areas of central Iraq. The Sunni Arab terrorists, and their al Qaeda allies, have been able to slow, but not stop, this movement. One after another, Sunni Arab towns are turned into Iraq towns. The prisons are filling up with more and more "known criminals" (people earlier identified as behind terrorist attacks.)
US troops fought the first battles in the cities while we built up the Iraqi military. As the Iraqi security forces get better and as we knocked the enemy down to levels the green Iraqi security forces could handle, we've moved on to the west into enemy-dominated territory. More Iraqi forces are following us in a persisting strategy of knocking down the enemy with American forces, securing the areas with Iraqis who can call on Americans for back up, and moving on to repeat the process. In addition, some Iraqi units are getting good enough to do the knocking down part.
This strategy is working. Of course, one big similarity with Vietnam that worries me is that even in Vietnam our strategy eventually worked as we learned from our enemy and moved to a strategy that secured the villages and cities. When we left, South Vietnam was pretty secure from insurgents. But our domestic anti-war movement succeeded in forcing Congress to throw away our hard-won victory by cutting off Saigon and letting the North Vietnamese blitzkrieg conquer the south.
So have patience. We are winning.