The American Numismatic Society is 50 years older than ANA. Members are more involved in the managment of the club. The ANS Library Catalog is online and it the one place to look for information about any numismatic topic. The library does not lend books to members via the mail, however. There are other drawbacks compared to the ANA. However, after 10 years in the hobby, I decided that joining the ANS was a professional requirement.
Most people are saying that the lending library is the best benefit of the ANA. The ANS you only get to look at the books if you go there? Sounds like it might be okay for people who are local to them.