Actually, about that...
APA Accreditation is pretty much the premier, if not the only Association of the United States, and has the monopoly on the political stance of students and practitioners in the field. Yes, APA has their benefits. However, 10-20 or more years down the road, it doesn't matter that much. APA Accreditation matters when you're in graduate school. Most programs are APA Accredited and is the standard for training and practice. It opens up APPIC internships, and makes it easier to obtain a post-doc as well.
Buuuuuut, the only real benefits is that you get to work federally and with the VA. Less loop holes to jump through. But when you've been practicing for a few years, that importance kind of dies off. So, if you want an easier time going through grad school internships and have a dream of working at the VA, yea--definitely go for APA accredited programs.
I've know Clinicians from both APA and non APA programs who are spectacular. Additionally, I've known clinicians from APA and non APA that were... Well, they had their licenses revoked.
In the end, if you want to help people and work in making the world a better place, like many of us do. Get the degree. But, make sure they're accredited by some form of agency (Higher Learning Commission, etc...). APA just provides a fast track for licensure, that's the major benefit.