The two organizations advocate for different groups of pharmacists and different issues.
ASHP (originally the American Society of Hospital Pharmacists), when it initially split from APhA, was organized to focus on the needs hospital pharmacy. The clinical model of pharmacy practice was really in its infancy, and the vast majority of its members were in what would today be considered staff hospital roles. Likewise, members of APhA were found, overwhelmingly, in staff roles in retail settings.
The growth of clinical pharmacy, both in the inpatient and outpatient settings, has created a new type of pharmacist (neither better nor worse, just different). Clinical pharmacy is concerned with a wholly different set of issues, that can't be properly addressed by either APhA or ASHP. Hence, ACCP was founded.
To those who say that organizations simply take their member's dues, then that's entirely your fault for paying them and not getting their money's worth. Become involved in an organization at a local, state or national level, and you'll see where that money goes. If you want to simply dump an annual fee and not bother trying to get benefit for it, then keep on going. I get value out of every dollar I pay, and I'm proud to say I'm a member of the organizations to which I belong.
ETA: I think your founding date is off, by the way. ACCP has been around since 1979.