It's not a direct port of the PS1 version, at least, not of the North American version, which recieved a handful of more convenient gameplay mechanics (sorting items, alerting you when Valkyrie's skills are removed when you equip a bow or sword, being able to equip characters outside the main party, etc). Otherwise, all the dialogue and voice acting is exactly the same, as far as I know.

Also, the PSP version is alot more stable, meaning you won't get that annoying buzzing noise in the background or freezing and so on like the PS1 version was prone to doing.

Also, this is a matter of opinion, but I did prefer the anime cutscenes more, even though the FMVs were very gorgeous.