In the short term DS will outsell PSP 2 to 1. This will be due to popular handheld software (Mario, Rockman.EXE, Yu-Gi-Oh, etc) as well as lower pricing and a launch headstart. PSP will likely have a higher installed base at the end of it's 10ish year cycle however, partially due to lower pricing accellerating sales/growth but also due to the fact that DS will probably only have 2-4 year lifespan. Neither platform will pass 55 million units total (what GBAs managed in just 4 years) however.