But one difference is noticeable almost immediately. Iraqi policemen are more visible in the streets of the capital Baghdad. And they appear to be doing their jobs with confidence and pride.
The Al-Khadra police station is based in Baghdad's northern district, close to the main roads linking the capital to neighboring Jordan and Syria, the restless town of Al-Fallujah, and the notorious Abu Ghurayb prison.
Police are working to ensure these roads are not used by suicide bombers and other terrorists looking to enter the capital.
Baghdad was plagued by heavy violence in the run-up to the transfer of power on 28 June. Since then, the city has enjoyed a week of relative calm, although some attacks continue.
Senior police Lieutenant Hassan Ali works at Al-Khadra. He tells RFE/RL the situation is improving. He notes that as recently as several weeks ago, attacks were common along the roads leading into northern Baghdad, and that police were dismantling between 20 and 30 explosive devices every day.
Now, he says, the police presence has increased: "We have more policemen on the streets, as you can see. They are at street intersections, squares. Everywhere, the police are present."
Still, Ali says, more is needed. Last year Al-Khadra had just 30 police officers. Now there are 130. The station has participated in a number of successful operations, including anti-kidnapping raids in central Baghdad that ended in the capture of some 100 criminals. But that is still just a start.
Farid Khalil, another senior lieutenant from the Al-Khadra station, says that the confidence of the police is growing: "We are controlling the situation because we have force, because we are counter-attacking and catching criminals and terrorists and detaining them."
Kahlil says Iraqi policemen have a better understanding of how to fight crime and terrorism in their own country than coalition troops. He says U.S. Army support was sometimes more of a liability than an advantage.
The Americans, he says, often released their suspects because of lack of direct evidence. Now, he says, people who are detained are not released so readily. He says his station has already seen a sharp drop in the number of robberies in the region.
"Now, when we arrest a man, we interrogate him. When the power is in our hands there is no possibility that a criminal will escape from punishment," Kahlil says. "The Americans, before, when they caught a criminal, they would let him back onto the street after a month or one or two weeks, and then he would commit another crime. We don't know what the purpose of that was."
In December, a number of Iraqi police officers told RFE/RL the U.S. troops were dealing with criminals in a way they considered "too democratic."
Khalil says now, if police detain a person they consider a potential terrorist or resistance fighter, he is transferred to the Iraqi police's counterterrorist department. Khalil says many non-Iraqi Arabs from places like Egypt and Eritrea have been captured in and around the capital carrying guns and explosives.
"Yesterday, in the Al-Ghazaliya [district of northern Baghdad], the police force had a conflict with three civilians in a car," he says. "They were carrying pistols with silencers, ordinary pistols and Kalashnikovs [machine guns], and they started fighting [with the policemen]. One of the police cars was damaged but the police were able to arrest them. They found explosives in the car."
Some observers say it will be very difficult to crush the Iraqi resistance. They say resistance fighters are attempted to portray their battle against coalition occupiers as a holy struggle or jihad against infidels.
But Ali, for one, says he will never call these resistance fighters -- who are killing more Iraqis than Western soldiers -- participants in a holy war.
"We do not call these terrorists here 'jihadists,' because they kill Iraqis,” he says. “You don't call a person who kills your brother -- or my brother, your mother, my mother -- a jihadist. This is not jihad, you cannot call it jihad. They are not Iraqis. They are Arabs [from other countries] and Westerners."
Ali also says he does not think a government amnesty would appease many of the resistance fighters. "These people are fanatics," he says. "They will not choose between amnesty and death, because they have already chosen death."