In my case, I run the Japanese PC versions of Ys I & II because I'm generally much more comfortable playing with a keyboard and mouse, as opposed to an analog stick, or even control pad (depends on the game, though). That, and the PSP versions of the games weren't even released at the time of my run (Japan or otherwise), and the PC versions are Japanese only (plus, I'd bet it's easier to record for the PC than the PSP).
Well I'm planning on attempting a run of Final Fantasy X-2 on the original Japanese version(Not International + Last Mission) since it's possible to get the Cat Nip accessory at the start of chapter 2, making the game much easier to break.
Japanese version isn't always faster but as many others have pointed out there are exclusive glitches plus shorter text. This is a moot point in games where you can skip cutscenes though.