The participating restaurants are pretty much the same (perhaps even exactly the same, though I'm not sure of that). You can't link the same credit card to two or more programs. You can belong to all three programs (I do), but you need a different credit card for each one. I think that the same company administers the program for various airlines.

Even if you dine infrequently in participating restaurants, you would lose nothing by registering your card with AA and perhaps gaining a few 1,000 miles. Once you've registered, the crediting of miles is automatic, though it takes a few days for them to be reported and it's wise to check occasionally to make sure that credit has been recorded.