Hi,
BA's Club World ( business ) is probably the best as the seats convert into a fully flat bed. I think some flights are operated by a 747-400 ( which should have the New Generation Club world- wider seats , AVOD) and some by the 777 ( older version of Club World but still with the flat bed. I would probably try to get on the 747-400 ( and on the Upper deck) as the Upper Deck feels more private and is only 2-2 across ( comapred to 2-4-2 on the 747 main deck and the 777). Some flyers complain about the large CW cabin on the 777 ( 48 seats) as it feels like a flying dormitory.
I personally prefer VS' Upper Classs with seats that convert into a wider and longer bed than BA but VS fly to LAX/SFO which would result in a connection being needed ( BA would fly direct)
Regards
TBS