Agree, not really possible because there are so many different types of training sites and their goals/foci maybe be completely different. Also, hate to break it to you, put they are all competitive. If you don't know about the nightmare that is the internship match imbalance, read up on it ASAP. As I was commenting early in another thread, although all are "competitive," certain programs are more competitive than others due to number of spots they have available, location (everyone want to live in CA, right?), and types of students they will attract.
For example, 200 apps for 8 spots is likely to be less competitive than 100 apps for 2 spots, right? Similarly, the applicants who apply to WPIC, MUSC, Palo Alto VA, and Mclean probably dont have the same training background/profile as those who apply to small community mental health centers in Utah. No offense, but a Psy.D candidate from Argosy is just not going to be competitive at sites like the Palo Alto VA because of the nature of the peer competition. And of course, you have to take into account your fit (both past experiences and future training goals) with the site when determining how competitive you will be within their pool of applicants. For example, having VA experience and having the future goal of being VA psychologist helps with many VA sites.
I agree that there is a common group of sites that are considered especially "prestigious." Not coincidentally, they are all very academic in nature (have mandatory or optional research components), have a reputation of providing high quality clinical training, and get tons of applications every year. Some of these are Brown med, Yale med, a couple of the Harvard programs (MGH and Mclean), Medical University of South Carolina Consortium, WPIC, UCSF med, University of Washington School of Medicine, Palo Alto VA, UCLA Semel, UCSD VA, Boston Consortium, University of Florida Health Sciences Center.