If you're going for privacy, I'd choose BA, as they have the almost-private cabin going. Also, you get a completely flat 6ft 6ins bed, and they even give you a sleeping suit (I think VS give you the same). BA has fantastic service; I've always found their stewardesses to be VERY professional, though, I do agree with someone who previously mentioned that VS have very good looking cabin crew, especially compared to BA.
BA's Terrace lounges are quite fantastic, too. The new First cabin feel in BA is quite luxurious, using materials like Connolly leather, walnut wood, velvet and cashmere fabrics, and I think by May, this will be available on the LHR-JFK route.
VS, on the other hand, has a more modern and sleek cabin look, and a more typical seat layout with 2-2-2 seating. Sure, you can have a drink at the bar, or a facial as your flying, but for what??? Do you really feel like having a makeover on a flight, or meeting some grogeous lady at the bar, only to retire to your seat later on??
The choice is yours!