I have flown all three and it depends on what you want. United's service in all three classes (First, Business, and Economy) are very good although the 767-200's are beginning to show their age, inside and out. They are clean and well maintained, but they are not as nice as UA's 767-300ER's. United's cabin crew in this market are usually friendly, professional, and caring. I've always had a good flight going to LAX and SFO and SEA for that matter, although the SEA flights are operated with A320's, not widebodies (used to be a 757).
American's advantages are MRTC, a greater chance of flying on a 767-300ER (I think AA has more of those going to the West Coast from JFK than UA, which has only one, to SFO, and none to LAX). Apart from that, the service on both carriers are virtually the same.
Delta's BusinessElite to LAX and SFO outdoes both the AA and UA product in terms of comfort, ergonomics, and amenities, but DL has far fewer flights, 3 nonstops max to each city, making it less attractive schedule wise. I've also found Delta's service in Economy to be average at best.
I think you'll find all three basically provide the same. Delta's Business Elite is the clear winner in the premium cabin, but all are fine choices.