Thank you for these bits of info! I really did not compare or think about the programs at all, felt just that Finnair is kind of a letdown these days.
So AA would be better in regards of getting miles out of AY flights but BA is ok, especially considering the Household account and the almost never-expiring points? Maybe we'll stick with BA for now then. Heathrow is hellish, but London is our favourite city. Don't mind travelling via London every once in a while.