Downquark1: While the British had the easier job (probably why the US gave it to us), it's basically army policies that separate why the British forces are better recieved than the American ones. I know one key thing i've read about is that America relies very much on technology (satelites, spy planes, etc), however the British have always relied on ground intelligence. Like meeting tribal elders, giving them incentives and getting good quality information back. This creates a better feeling among the people, than cutting them out the loop. But that is not the case totally though. America's reputation is so bad that I don't really think they anything they do to win hearts and minds would work.
Apparently though, i've just heard that some British soldiers (2 I think) are in trouble over alledged photographs. One was of a guy urinating on a prisoner. I can't remember what the other one was. It is in tomorrow's Mirror..
http://news.bbc.co.uk/1/hi/uk_politics/3675215.stm