Unless I'm mistaken, the British are deployed to the South in the far friendlier Shiite areas, whereas the U.S. troops are bearing the brunt of the Sunni revolt. Apples and oranges. No armor in the U.S. areas was resulting in soldiers assasinated in grocery stores.
It depends what you mean by "friendlier". I don't think getting blown up is friendly, but I take your point.
However, Britain and America have always had different tactics which actually helped Britain when we defeated the Argentines on the Falkland Islands.
The Argentinians were trained by America, and supposed that Britain being friendly with the US would also use the same tactics as the US. So they expected a full-frontal assault on the main bases. However, British tactics have always been different and the British Army landed in the opposite direction, trekked for miles to surprise them from behind.
Maybe the differences compliment each other.