Quoting from the Phi Beta Kappa website (
www.pbk.org):
"Phi Beta Kappa is the oldest and most respected undergraduate honors organization in the United States. The Society has pursued its mission of fostering and recognizing excellence in the liberal arts and sciences since 1776."
Furthermore, from the FAQ at the same website:
"Candidates are nominated for election by their chapters and cannot apply for membership. Students interested in Phi Beta Kappa are encouraged to contact the chapter officer early in their academic careers for guidance on requirements and curriculum."
Phi Beta Kappa, Sigma Xi, and Tau Beta Pi (and various other discipline-specific honor societies) are by no means mutually exclusive. I wouldn't shun an invitation to join any one just because you already belong to another, if I were you.
Think of PBK as the undergraduate, multidisciplinary equivalent to Alpha Omega Alpha. You wouldn't turn up your nose at THAT one, would you?!
At my school, the chapter sponsored a lecture series each year that brought some very interesting, prestigious scholars to campus. The national organization offers some scholarships, research grants, etc. They also publish a journal (you have to subscribe to this) and a newsletter (comes free of charge once or twice a year and contains lots of book reviews).
Nutshell: if your school has a chapter (not all do--the school needs to meet certain standards and apply for a chapter), and if you've got the grades to get in, do it. You never know what doors it might open.