I can only really compare Addison Lee with Airport Direct, as I haven't really used any alternatives. Addison Lee is more expensive, but you do get a more formal, predictable service (drivers wear suits, they drive a standard, high-end MPV, etc.) WIth Airport Direct, you still get a good service, but it's much more on the 'reliable minicab service' level than AddLee. I've never been let down, or had cause to complain with either.

There are a couple of alternatives - IIRC, there's a company based in Chelsea which gives very good rates to addresses West of the Centre that was mentioned on another thread, but I don't have the details, I'm afraid.