Will you get a lower quality of education at a freestanding professional psychology school? Of course there is no easy answer and a lot depends on what you are seeking from your graduate education and the school itself. I have a somewhat unique perspective on the issue since I have doctoral degrees both from a large state university and a small regionally accredited professional school.
In general, the research training I received at the state university was light-years ahead of what was offered at the professional school (so much so that I actually was asked to teach research methods at the professional school I was attending). The clinical training in the state university program, while wider in scope, was more technique oriented and without a lot of depth. My sessions with my clinical supervisor were again almost exclusively geared toward the technical aspects of doing psychotherapy and testing/assessment.
At the professional school I attended everything was much more geared to clinical practice. All of my professors maintained professional practices and derived the majority of their income from them. The professional school I went to was highly psychoanalytic/psychodynamic in orientation. Therefore there was a strong coherence between the techniques and the theories that were taught. And, most importantly the theories drove the techniques. In the university program I felt like I was rummaging around my bag of technical tricks for something that might work with a specific client. At the professional school any technique I used needed to make sense depending on the theoretical understanding of the person I was working with. While the professional school I attended would never turn out great researchers or psychometricians, it did produce thoughtful, deeply grounded, and consistently good psychotherapists. My relationship with my supervisor was also far superior. I received very intensive 1-1 supervision that analyzed my reactions to doing psychotherapy or being a psychotherapist (counter-transference, developmental issues etc.). As a result of this I have come to believe that without this kind of supervision you cannot really properly do psychotherapy – counseling maybe, but not in depth psychotherapy.
Over the years I have thought about the issue of university versus freestanding psychology schools I have come to realize that my experience may be unique. Some university schools certainly teach psychotherapy in an in-depth way while many professional schools give their students a bag of tricks and send them out the door. Many psychologists hold the view that all freestanding professional schools are bad and all university programs are good. I do not believe that this is true and this was not my experience, BUT you will need to carefully research the schools you are thinking of attending!