The PSP has never outsold the DS outside of the occasional month in Japan when a game like Moster Rancher or Final Fantasy is released or the console is redesigned. In those "first 1-2 years" you are talking about, the Nintendo DS became the fastest selling handheld game console in history.
it was outselling the first year as DS wasn't well supported then and Nintendo had introduced Gameboy Micro so they weren't supporting it well
do take in accont that PSP's release was spaced out and DS released before PSP.if you look at the first year sales of respective regions,PSP is ahead
when Nintendo discontinued Gameboy and went fully behind DS,then it started rising.PSP's piracy helped a big bit too almost all the developers pulled out support