Been away a couple of days ... just catching up. I've flown to and from LAX a lot BA, Virgin, American, Air New Zealand.
BA and Virgin flights - sometimes one is cheaper, sometimes the other as you've discovered. Personal preference (and experiences) point me to Virgin and NOT BA. The time I flew Air New Zealand it was great and you MAY find better availability / prices ... It's their NZ -> LAX -> London flight and being based in New Zealand they can sometimes have problems filling the leg that doesn't start or end in their home country.