If you are originally from the US and only temporarily in the UK, AA may be preferable. Non-transatlantic BA flights can earn mileage on AA. Discount coach flights on BA only earns 25% credit (including BA transatlantic flights), whereas all AA flights earn 100% credit on AA. Thus, if your longest segments are likely to be on AA metal, it may make sense to choose AA as your 'home' program. Also, most inexpensive fare classes on BA do not count at all towards elite qualification in BA Exec Club, whereas all mileage eligible flights on AA and OneWorld partners count towards elite qualification (again, very relevant if your longhaul flights are on AA). AA also allows mileage to be used to upgrade almost any fare class on AA (i.e., even a cheap transatlantic coach ticket can be upgraded), whereas BA is more restrictive.

For one who is US/UK based, I would expect that EI, IB, CX and AY are significantly less useful FF programs. Airlines tend to give the most recognition to their 'home' elites, so it is generally a good idea to focus on an airline that one will be flying with some regularity.