Ah, alright, thought the whole exploring the eastern and western parts of the world was an indication of previous games.
I have the other ys games on steam but I enjoyed playing it on my vita so much I'm thinking of getting the PSP versions. Should I? Is the steam versions improved over the PSP ones?
Origin is exclusively on PC/Steam, and Seven is exclusively on PSP (yeah, Chinese port, not getting into that).
For the ones you have options for, I & II Chronicles+ on PC is better. It basically offers everything the PSP game does, plus lets you use the wider FOV/traditional border from the previous Complete version. PSP version also mildly annoying loading times compared to the PC version. Not super awful, but they are there and last a few seconds.
Oath in Felghana could go either way. The PSP version has voice acting and some non-essential extras. Gameplay changes make it a bit easier, since when you die you restart in the same room instead of going back to the last save point. It also adds a double boost mechanic instead of just having the normal boost. PC version looks and runs better, and it's a bit more challenging due to the aforementioned gameplay changes.
Really, apart from Ark of Napishtim all the Ys games are fine on PSP, though I prefer playing them on PC. If you play Napishtim definitely get it on PS2, or hold out for XSEED's inevitable release of the PC version.