I am not familiar, but, cutting the "changes" section out of a review:

https://www.rpgland.com/games/hoshigamiremix/review.html

Remix adds various, easier difficulty levels, new character art, redone music, a new character, and an overhauled localization.

Another problem with the game is the extreme lack of portability. It is a DS title, and as such should be capable of being played for small amounts of time at once. Unfortunately, there is no suspend feature to allow for saving while in battle. Factor in that the average battle can take 20-40 minutes and that sometimes one battle immediately follows another with no break for saving, and here's a game that is not at all good for playing on the move.

So going entirely off that, it sounds like the remake is probably preferable, but it might not be a good idea if you plan to play the DS game as a "mobile" game --- dropping into the thing for a few minutes while waiting in a line or something.

Not familiar, but a quick Google indicates that the DS version improves somewhat on the PS original. It's still considered a terrible game though.

I played the DS version and found it to be kinda bland and cookie-cutter. Can't even remember anything specific about it honestly, I just remember it being a very forgettable game. Couldn't tell you if the PS1 version was any better, but I doubt it.