If you sign up for Alaska Airlines frequent flyer program, you can earn miles on American, British Airways, Delta, LAN, Air France, Air Pacific, Cathay Pacific, Icelandair, KLM, Korean, PenAir, or Quantas, and you can redeem on any of the above. Then you don't have to choose between Delta or American, you can do both, and LAN has good coverage in South America.

It might be harder to earn and use status though, as only the higher status levels give reciprocal benefits with Delta, and a reciprocal agreement with American is still being worked out.