BA have an evening departure from LHR, which while you would have a long layover there would help the jetlag management. Sleep for a few hours from LAX, a short day in London and then a long nights sleep on the way to DEL. Coming back you are stuck with the 3:25am departure. While it is pretty grotty in the airport at that time, once onboard you can sleep easy for 8 hours.

I can see the AA flight as more convenient (though ORD can be as big a pain to connect through) but I wouldn't fancy 15 hours in AA's J seat. You might however, as BA's (only 6ft long) gets mixed reviews from 6ft6 tall people. If you sleep with your legs curled up, no problem. If you sleep on your back, not so good.