This will be deeply subjective as they both have their pros and cons. I've done both, and prefer BA First.

I like the Flagship First check in at LAX and JFK, and I enjoy the Flagship First Dining. But the onboard experience on AA is not great IMHO. The 'suites' have no privacy, the IFE is small compared to BA, and the service is not as friendly. The thing I really hate, and I know this is a proper first world problem, is that you're separated from the people in business by a see through net curtain (I asked about this, apparently it relates to post 9/11 security changes and visibility down the plane).