Even though the OP lives in Finland, I'd still recommend using AAdvantage for mileage accrual... on average, it's easier to accrue miles, and redemption levels for AA awards are lower. Furthermore, with the OneWorld saphire status that the Platinum Challenge will afford the OP, he'll earn even more miles (100% bonus) than would ever be possible for a similar trip under the AY programme.

When I lived in the states (pre July-2003), I accumulated my miles with BA. Now that I'm based in France (and BA has changed mileage accrual levels), I earn with AA. Many people do the same... in particular, many Australian friends of mine started earning with AA after the QF program changes. But this is getting a bit OT.