psp, if content-identical to the DS version, then should be the clear and superior option in everything: aspect ratio, resolution, etc, therefore see absolutely no reason to play the DS version.
PSP is glorious 2D sprite work, not blocky giant polygons like the DS/mobile and successors. It's definitely the best looking version. IIRC, it uses the GBA translation, but with some of the DS translation nonsense thrown in, like "Eidolons", a word which has no place in FF4.
I really don't care for the DS translation, it's far too wordy and pulls shit like that out just because. The voices are bad as well, especially Cecil. I'm not saying don't play that version, or it's bad, I'm saying IMO the PSP version is a lot better.
The one thing the DS version has in spades is extra difficulty. If that's what you care most about, yeah, go for that or one based on it.