Let's see ... I've flown that route with American, BA, Virgin and Air New Zealand.
Personal ranking:
1. Virgin
2. American
3. Air New Zealand
4. BA
Reasons:
Every airline is subject to occasional delays / cancellations, but in my experience of such events, Virgin have always treated their customers, even cattle class ones, as human beings. A couple of nasty experiences with BA have shown me that they don't quite take the same attitude - old experiences, but I don't know that much has changed from seeing some of the TV coverage they've had this year. The other two I can only recall 1 or two flights each, both excellent and no makor problems. Horrific check in line for American though, and the Air New Zealand flight is the first (or second) leg of their London to New Zealand service, so in LA you're joining not a totally clean new plane, but a plane and passengers that have already completed a longh haul leg.
P.S. I have also flown indirect using United (domestic), then Transworld and PanAm (atlantic crossing) on this route .... but I think that comments would be irrellevant to the question