The remakes for Pokémon Generation IV seem to be aimed at addressing Diamond/Pearl's most obvious shortcomings.
Ahead of the release for Pokemon Brilliant Diamond/Shining Pearl, developer ILCA and publisher Nintendo have marketed the two remakes as faithful adaptations of the original Generation IV games. I recently attended a preview event for the duo where I got to see B. Diamond in action, and although these remakes look faithful to the original games, I'm not so sure that they'll feel as faithful. If anything, the changes made in these remakes seem to make for a far more approachable experience--I think players are going to find these games to be a lot easier to get through than the original Diamond/Pearl.
In terms of overall structure and presentation, yes, B. Diamond/S. Pearl are faithful adaptations of the original Diamond/Pearl. Unlike Sword/Shield with its over-the-shoulder perspective, realistically proportioned characters, and occasional free camera moments, B. Diamond/S. Pearl is presented in Pokemon's traditional top-down isometric perspective with a more chibi-like visual style and no free camera.