Are you taking the daytime or overnight service to London?
If I'm taking the overnight, I'm essentially looking for a decent sleep and minimal service on board. With BA/AA I can eat and drink pre-flight in the lounge, board the flight, recline after take off into horizontal mode and then hunker down for some shut-eye until top of descent. The eastbound flight to London is a short one (equivalent to a LA-NY red-eye) so I'm not about the full service if I'm taking one of these, I'm all about the comfort. On arrival I can also go the BA arrivals lounge for breakfast after baggage reclaim which beats anything I'm going to get on board as well as being able to get a shower before heading out from the airport.
For a daytime flight I'd probably want to watch some TV and partake in the onboard service a bit more in which case B6 becomes more appealing. I don't necessarily want or need a lounge on an early morning departure in which case B6 suddenly becomes more compelling.
I guess it comes down to what parts of business class are important to you. Be that lounges, on board service, points, price. Only you can decide.