It is not an issue of prestige. After you are licensed, almost no one will care if you have been to an APA approved Internship or not. (Although some government jobs for psychologists will want you to have an APA Internship.) The real issue is that in some (many) states, if you did not go to an APA approved school, or did not go to an APPIC internship, you are going to have to demonstrate to the licensing board of your state, that your training really was up to par. If you go to a non-APA school, you can still get an APPIC internship, but if your Internship is non-APPIC, you mighthave a harder time getting licensed.