I think many people's most significant point about the ground service - and reason to prefer LH despite a more dated product on board - is precisely for the reason above.

Whether you're in F or Y, BA gives a shiny-card-holder about the same amount of "stinking airport" experience. Security queues that really don't give any meaningful priority whatsoever. The same compliance cutoffs. The same free-for-all boarding process. The same waiting around the baggage carousel for bags that, if priority tagged, will invariably appear last. The same bus rides to/from remote stands. All of which amounts to there being precious little time saved for those who book F over those who book Y. Let's not even start about what happens if, like many travellers, you need to make a connection at the carrier's hub, which is something BA at LHR still manages to make as un-premium and unpredictably slow an experience as possible. (Although admittedly it has gotten somewhat better in my experience over the last 12 months or so)

What LH seems to have done very well, on the other hand, is both reduce the amount of time an F passenger has to spend at the airport itself, and make what little time you do have to spend at the airport as un-airport-like as possible. This is accomplished by moving F pax away from all the queues/desks/other checkpoints, handling your bags for you, driving you individually to/from the aircraft, so that not even a bit of time is wasted with the boarding process. If you're making a connection, it seems altogether plausible that you would cut away a lot of wasted time (and discomfort) by connecting as an F pax on LH rather than putting yourself through the shambles that is FCC at LHR T5. I'm not sure how much less the MCT is on LH, but whatever it is, I also get the impression that you can usually bank on it working, whereas with BA I frequently book the second connecting flight so that I don't have such a high probability of missing a connection when I'm playing planes, trains, buses and queues at LHR.

At least, that's my impression. I've flown BA F quite a few times in the last few years, but my last F on Lufthansa was too long ago for me to comment on anything other than the fact that the seat then would still be the same old seat now!