A week of fighting in Fallujah has left over 2,000 anti-government gunmen dead or captured. American and Iraqi casualties (dead and wounded) totaled less than 400. The gangs that dominated Fallujah for months had turned the place into a complex of weapons dumps, torture chambers and holding cells for kidnap victims. The gunmen took over peoples homes by force, and generally terrorized the population. American commanders noted that the gunmen in Fallujah had little in the way of leadership. The resistance was largely by young guys with guns and no commanders. Apparently the leaders of the gangs and anti-government organizations slipped out of Fallujah and just told the people they left behind to put up as much resistance as they could. The resulting battle was very lopsided, with some 25 gunmen getting killed for each American or Iraqi soldier lost. There was no reason to stand and fight in Fallujah, except to provide propaganda opportunities ("the evil foreign occupiers are murdering the valiant Iraqi freedom fighters.")
Having lost their base and rest area in Fallujah, anti-government forces are now trying to take control in other towns. Using the same tactics they originally used in Fallujah (driving out the police and then terrorizing the local population), they have found the resistance much stronger than in Fallujah. The attempts to dominate over towns has failed, and the anti-government forces continue to take heavy losses. When the gunmen come out to fight, they are quickly spotted by air reconnaissance (especially UAVs), and hit from the air and ground.
The Iraqi police in these Sunni Arab areas continue to be poorly trained, led and motivated. The Sunni Arab police too often just run. To a lesser extent, so do Iraqi soldiers. Such cowardice is traditional. The concept of "stand and fight" is not widely accepted in Iraq. This was a particular problem during the 1980s war with Iran. Saddam had to use all manner of incentives, and terror, to get Iraqi troops to effectively resist Iranian attacks. Had Iraqi troops not been able to take advantage of the waterways in the swampy battlefield, and had not chemical weapons been available, Iran would now be running Iraq (as it has done for most of the past few thousand years.)
The gunmen in Fallujah did so much stand and fight as run around trying to set up ambushes. Their problem was a lack of good tactics and leadership. They wanted to fight, but didn't know how, and got killed in large numbers as a result. The gunmen do adapt their ambush and roadside bomb tactics when they find that something obviously doesn't work very well. But coalition troops adapt quickly, quicker, in fact, and the gunmen continue to fight at a large disadvantage.
The war of wits, and the differences in training and leadership, have been the key factors in the Iraqi combat. The Sunni Arab community, which is the core of the anti-government fighting forces, is more concerned with regaining power than in reforming their inefficient and ineffective combat and political techniques. With great effort, American trainers have created some Iraqi infantry battalions that can fight. The war in Iraq comes down to which tradition will prevail; that of terror, or of good training and leadership.