In Afghanistan the mujahideen had a favorable kill ratio over the Soviets, when equipped with Lee-Enfield rifles, which disappeared when the Enfields were replaced with AK-47s and AK-74s.
The theory was that when they felt outgunned, using the old bolt action Lee-Enfields, they engaged only from a distance, using cover and surprise to compensate for what the felt was a deficiency in their arms.
When they felt equal in armaments, they engaged from close range.

Probably the same thing is happening in Iraq.

Since the insurgency feels outgunned by the US, they would pick their battles carefully, avoiding what they feel are the strengths of the US forces, and focusing on their weaknesses.
IEDs would be the weapon of choice, as an IED attack rarely results in insurgency casualties, it's like their standoff weapon.
I'd assume the insurgents may feel a bit more daring against the Iraqi Army, and engage them more openly, so the Iraqi Army would probably do better against the insurgents than the US forces in body count anyway.

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“ The subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state.”

Adam Smith , The Wealth of Nations 1776

"We have always known that heedless self-interest was bad morals; we know now that it is bad economics"
FDR's second Inaugural Address