Uli,
AA.com will not give you all the info that you need so easily. Go to American Airlines forum on this board and search there. An excellent alternative is to check out websites by our expert
FewMiles who has all very well summed up at
http://plaza.powersurfr.com/fewmiles/AA/index2.html
and
http://plaza.powersurfr.com/fewmiles/oneworld/
Top status on AA is EXP (Executive Platinum) same as 1K on United. EXP can be achieved by flying 100,000 miles in coach/economy or if you want to fly in F then just about 66,000 miles. Alternatively you might choose to do it the hard way and fly 200 segments at a minimum of 500 miles each. All AA fares earn you miles just as well on partner airlines. On top of this you earn class bonuses and promotion bonuses. Putting it more simply, just about every time I do a roundtrip between Europe and Australia in "J" I get about 120,000 miles which is enough to fly "J" between Australia and Europe on CX! In other words, buy one get one free!
As far as BA is concerned then it might be a very good idea to do a VERY deep reading of their forum. It is not as good as it may sound at first glance

. And they apparently don't comp.