BDSP was a terrible remake that was farmed out to a random porting studio. It's one of the lowest effort remakes I have ever experienced.
One of the biggest issues is BDSP added modern EXP share where all your pokemon gain EXP every battle.This caused a huge problem for BDSP because they didn't re-balance the game to account for you gaining much more XP than the original developers expected. The game is completely trivial because you become unreasonably over-leveled when playing through the game normally.
Platinum also added extra content to gen 4 beyond the original Diamond and Perl. None of this content was added to the remaster. If you are wanting to play gen IV and have hardware that can run it, Platinum is the best choice.
BDSP are 1:1 Unity remakes of diamond and pearl, for better or worse. Platinum just had some small quality of life upgrades and both the legendaries.
Also, BDSP aren't made by Pokemon Company, I enjoyed the games but artistically it's just not Pokemon. If you told me BDSP was a fan game, I'd believe you. It's cool to see a 3d chibi take of Pokemon but I love the art direction of the DS games far more.
I've consistently heard that the gameplay fixes of Ultra make the game objectively better, however they make some weird ass story changes that ruin the story of a very dialogue heavy game.