BA has flat beds and going east is easier on the body for jet lag, for most people. SAN-ORD-DEL on AA is 9207 miles; SAN-HKG-DEL on CX is 9700 miles; SAN-LHR-DEL on BA is 9675 miles. Surprisingly little difference, giving you lots of choices. Using evips on ORD-DEL is reputed to be the hardest flight in the AA system, fwiw.

BA J is the only one which has flat beds, which has a big advantage in this case (but you cannot earn AAdvantage miles for BA transpacific; I solve this problem by crediting BA flights to QFF). I would probably go for a OWE (Round The World) ticket, and fly BA SAN-LHR-DEL (though I guess you have to go via LAX now, I think BA dropped their SAN flight) and then CX DEL-HKG-LAX. The OWE gives you up to 20 segments, allowing you to take side trips in Europe/Asia/US for the same price (things like a sidetrip to Aruba or Costa Rica). If that isn't an option, BA J really does work well on this routing and seems to be the best choice, despite the havoc that is LHR at the moment.