There is no comparison.
SWISS outclasses American Airlines in all aspects.
From the flat seat (it's not horizontally flat though), to its inflight service, food, and personal entertainment system. And you know what? The plane feels CLEAN, refreshed (and that includes the cabin crew), and new. On the other hand, AMERICAN's planes feel old, dirty and tired (and that also refers to the cabin crew). Business Class on AA is just dull.
Enjoy while you can as SWISS is to be bought over by Lufthansa and will eventually be intergrated into the Star Alliance. I believe it's a partner with AA's AAdvantage programme now.