There are so many variables it's hard to know what to recommend. If your main route is still LAX-LHR and you fly paid first, then you should probably stick with oneworld since VS and NZ only have biz class and all other airlines mean you have to connect somewhere.
If you are flying paid first within the US, then you don't need the upgrades that could come with AA's EXP status (note that these are getting harder and harder to come by). in that case, BA might still be better since it will save you the cost of an Admiral's Club membership. On the other hand, if you are USA based, using a joker as BA GGL means you have to go through London to get anywhere which might not be the most convenient routing for vacations.
Delta has good service but Delta's FF program is not very good (meaning you have to use astronomical amounts of miles to get award tickets).
For me, service in IRROPs would be important. If you're flying more within the US, then being EXP might be better than being BA Gold but I would think you would still get good service recovery when things go wrong.
Last edited by eefor jfp; Jan 4, 2020 at 1:37 pm
Reason: changed VX to VS (thanks Mwenenzi; VX was Virgin America; I should have looked it up).