From my understanding All APA are APPIC
approved.....but not all APPIC approved sites are APA-
acred. CPA is a state level acred.
Realistically: APA > APPIC > CPA.
This has been writing on a bit in regard to APA v. APPIC with a bit on CPA.....as they more than any other state have people pushing CPA for those who want to stay local. There are so many people trying to go/stay in CA, it has created an artifical market for CA.
APA won't close any doors for you. APPIC closes a few doors (VA, some of the more competitive jobs, a few states). CPA is more limited and you may have problems getting licensed elsewhere, but YMMV.
Here is a thread that has some info:
http://forums.studentdoctor.net/showthread.php?t=391523
*edited to clarify*
CPA = California Psych Assoc
Canadian Psych Assoc = APA in regard to training standards (in the eyes of most everyone). A number of years ago there were APA+CPA approved sites, but that is/was being phased out. There are far fewer Canadian sites too.