It really depends on your specific routes. Gaining Sapphire elite status (for lounge access) is generally much easier on BA than AA. Being based in the UK, BA miles are also easier to accrue though non flying means (Tesco and Credit cards add up quickly) that you can use for upgrades. TATL upgrades can also be signficantly cheaper on BA (you have to buy premium economy to upgrade to business -WTP to Club, whereas AA you can upgrade from any economy fare with a higher mileage requirment AND CASH Copay). Non Upgrade flight awards are generally much cheaper on the AAdvantage program.

If you are willing to pay for premium economy (WTP) on BA and are interested in upgrade awards only, then BA is probably the better program for you. If you are interested in awards only, then AA is the better program.

If you had a chance of top tier, then I would say AA is all around a better program, but at your level of flying, there is not a clear cut winner without more specifics on your travel pattern.