There is much to weigh up. Here's my own cursory comparison.

Earning opportunities:
AAdvantage is a great programme but it is generally far more constrained for UK members than it is for US members. In the UK earning potential is limited to airline partners, hotel partners, car rental plus two affiliate credit cards (MBNA/AAdvantage Visa and MBNA/AAdvantage Amex)

With Executive Club you can also earn through everyday grocery shopping (Tesco) and eShopping via BA's eStore portal.

Earning through the pursuit of flying is less clear cut. Whereas AAdvantage programme generally matches the EC mile for mile on travel with AA, BA and IB with discounted economy tickets, earning is higher with other partner carriers (100% AAdvantage versus 25% EC). If you are travelling in flexible economy, its a wash. In Premium Economy, Business and First class the EC excels.

The EC also has the benefit of more transfer opportunities - Amex Membership Reward points, Starwood, and closer to home transfers from the consumer (Ch)Avios programme.

Spending:
Other than short haul redemptions it is universally cheaper to redeem on AAdvantage than it is with the EC. However, when redeeming for BA flights, the cost is about the same. BA levy nominal fees for changing/cancelling redemption tickets, AAdvantage fees are significantly higher. Also, once you become a top tier member these fees are waived on both programmes.

What have I missed?