My biggest gripe with BA F is the lack of tarmac service (which LH/AF both do very well) and true premium transfers..
If you're connecting over LHR, you have to schlep to the connection zone and then back through the "premium" security which is a zoo. Its hardly a "first class" experience.
If you're flying LH, (and esp if you're at a remote stand) they pick you up in a nice car, whisk you through formalities and you end up right in the lounge. Personally, I found it most unpleasant transiting LHR, though, once on the plane I found it to be a very pleasant experience.