We always use Addison Lee to Heathrow but don't tip. However, this is purely because I am following British unwritten custom, which is tip black cabs 10% but not to tip mini-cab drivers. There is no real logic to this, both are self-employed drivers.

I did read somewhere on the internet that AddLee drivers are badly screwed by the company if you pay in advance by credit card in terms of the % of the fare they get to keep, but this may just be rubbish. I've used them loads of times now and never had a problem - always on time, always brand new vehicles with built-in child seats.