I fly quite a bit on both airlines, and it's hard to say there's a big difference in service overall. UA is definitely more convenient out of SFO. Domestically, UA flies more non-stops and uses international aircraft for some flights, which is very nice if you upgrade. AA has too many Super80s.

Internationally, UA covers both Europe and Asia well with many non-stop flights. You can also use UA upgrades on LH on a stand-by basis. I also like UA's business class seat better than AA's. AA does not fly anywhere internationally out of SFO (without at least one connection).

You mentioned you fly CX. CX has better service than UA, but you must always connect in Hong Kong. So it really depends on your preferences.
What I like about AA is the OneWorld alliance. You also get your 100% Platinum bonus on OneWorld, but do not get this on Star Alliance (except on LH).