AED and PBK are two totally different situations. AED is a pre-med honorary (at my school it doesn't seem to make a difference if you surveyed pre-meds who got accepted and were in it v. those who were accepted and weren't) and PBK is an honors society which is an award given via a selection committee at your school, usually when a person has reached Senior status by credits (criteria varies by school). Phi Beta Kappa is invitation only while at my college anyone can join AED provided they meet a certain GPA and participation levels.
Also, PBK isn't your standard honors society. It was the first one founded in the U.S. (1776) and has counted some pretty amazing people as members. Many of the other honors societies you hear about in the mail have been founded to sell books to people who like to see their name in print.