Probably BA, but there you need to fly on 4 BA-metal segments. BA awards (with the exception of some short-haul trips) are generally more expensive (in mileage terms) than comparable AA awards, owing to BA's requirement that multi-segment awards are charged on a point-to-point basis rather than an origin/destination basis. For example, using BA Avios, IND-xORD-xLHR-JNB (one way) in J would cost 99,000 Avios, vs. 75,000 AA miles. 9,000 of those Avios would be needed just for the IND-ORD segment; using AA it would be all-inclusive.

Elite status in the BAEC comes from tier point totals, not miles flown, with discount economy earning very few TPs, full-fare ("flexible") economy earning more, but not as many as business or first class. You need 600 TP or 50 flights to earn BAEC Silver (Oneworld Sapphire = AA Plat) which might be tough given your flying patterns.

You wouldn't get upgraded on AA flights; however as BAEC Silver you could use AA lounges on domestic flights, which you couldn't do as an AA Plat.

Probably best for you to research the programs some more on the AA or BA boards. I do think, however, that based in the US, AA would be the way to go.