Be sure to compare your ticket purchase patterns with the reward pattern of the programs you're considering. For example, of the two I was realistically able to consider, AA is more generous to passengers on discount economy tickets (which I use when possible) than BA. On BA I would have no status on this point, whereas my 100,000+ miles earned me AA top tier. Someone who generally flies in paid first or business class might prefer BA instead.

If you do much trans-Atlantic flying and are considering BA and/or AA, keep in mind that you do not get any credit in those programs for flying the other on those routes. This does not apply if you are enrolled in any other OW program or flying on any other OW airline.

Not that I want to support the competition, but from a practical point of view since you're based in in Germany, have you considered Lufthansa and Star Alliance? If a choice of non-stops to North America matter to you, that would (sadly) be the way to go.