BA on its Olympic Dove Plane:
Doves are internationally recognised as a symbol of peace and social unity, and were also used in previous Olympic Games ceremonies, including the last London Games in 1948.
Virgin on its SF Giants Beard Plane:
The aircraft sports a beard, as a nod to the facial hair-friendly hometown team... Those who happen to catch a flight on the aircraft also have the chance to score [free air travel]: Virgin America is inviting its social media fans to send in their best photos of the new Giants-decaled plane using the hashtag #flythebeard.
The BA plane is pretty subtle. I don't think it even has a logo from either London 2012 or the Olympic Rings on the plane (I'm fairly certain BA has rights to use both). While it feels quiet, BA uses the sponsorship in an unconventional way. The airline associates itself with an inspirational, noble human value with greater fanfare than it could have achieved with a paint job alone.
The Virgin approach is more tribal, unexpected and humorous, playing off a somewhat-inside joke: the "Fear the Beard" slogan that surrounds Giants' pitcher Brian Wilson.
As an aside, both airlines also tout menus and in-flight content related to their sponsorships.
Who fared better?