So I bought it over the weekend, I've put a few hours in now so I thought I'd just post how I feel about it.
I've played this before on the DS, the PSP is slightly nicer, benefits:
o The 16:9 really makes a big difference. Although a little funny without the other screen (although I am damned if I remember if it did anything useful). The DS version now feels a little squished, where there's enough room for the battles - with a good distance between team and bad people.
o The chip music - although I love chip music (I also chip music myself) the DS music is lovely and the chip music is really a downgrade. It would have been good to have chipized remixes or something, the chip music versions sound a little flat.
o Framerate - it doesn't choke like it used to on DS, in fact, the resolution makes it looks very high rez, I think that some of the textures dont' look so muddy (or upgraded).
o Auto Battle - THIS, the reason to own this version. Although not as good as the "hold the button down and do what we did last time" on Final Fantasy I+II PSP, the auto battle is great, switch on/off with Select. Annoyingly, you still need to press circle when on the results screen (obtained 2 gill, received 2 EXP! Job increase etc).
So there you go. I played FFIII when it came out on DS so it's great to play this again.