Interesting that the media bias site grouchy linked as the BBC as a left of center bias. I know a lot of lefties who would argue it is has a right wing bias...
Yes, I've noticed all sorts of people of all political persuasions claiming that the BBC is biased against their particular views, it's probably a sign that they're not too badly biased in any direction isn't it?
Personally I trust the BBC not to lie and not to put too much of a spin on things. I trust the Guardian to accurately pick out the facts that suit their agenda and to cover a story in enough depth that it's easy to go to the source and find the real story.