You should have no trouble grinding, as previously stated, in any of the main series games, simply because the developers try to avoid it. So long as you attempt to battle most, if not all of the trainers you encounter throughout the game, you should have no trouble with any of the battles. You should try to avoid intentionally avoiding trainers, for the experience is immensely helpful. However, some grinding may have to be done before facing certain Gym Leaders based on your choice of Pokémon. Quite a bit of grinding will also have to be done in almost every game however upon reaching the Pokémon League.
Now back to the question... Platinum is indeed a game that requires less grinding. As (once again) previously stated, the entire game difficulty was basically scaled back, and the story was sped up, due to the slower nature of Pokémon Diamond/Pearl. It allowed for a more enjoyable experience. If you are not a fan of grinding, I would recommend playing Platinum over D/P, though I will stress that the difference is rather minor, and all games are excellent.
FUN FACT
The infamous Victory Road was actually put in place for the player to in fact grind. The common rock types found in these caves were meant to benefit any player, providing a type disadvantage to the three starter types Grass, Water, and... Fighting? Yup, Fighting, the most common secondary type to the Fire starter. Ever thought why?
