When choosing between Pokemon games, decisions are often hard to make. But this isn't one of them. For me, choosing my favorite out of the two options here is one of the easiest decisions to make. Below is my personal opinion on the matter.
Platinum is a much better game in every possible way. While I never disliked Diamond & Pearl, there were some things they could have done better. The Sinnoh Dex didn't have all non-legendary Sinnoh Pokemon, the Poketch only had one button, the surfing speed was slow and the Pokemon distribution was lacking at places, among other things. Fortunately, Platinum fixed all of these things, in addition to keeping everything D/P did well. It also added several fun new features like the Battleground, the Distortion World and the new Wi-Fi features. In addition to this, it brought back features from previous games like the Battle Frontier (with new facilities), Move Tutors, a stronger Elite Four on subsequent visits, Gym Leader rematches and more. There were more legendaries to catch as well as more things to do overall. The story and the characters were massively improved as well. The story and the game itself wasn't a rehash of a previous game, which was welcome. D/P didn't have any problems with training spots or the level curve, but Platinum improved on them in these areas as well, making training Pokemon and completing the Pokedex as easy as it could be for its time. Sinnoh is a great region, one of my favorites, it has a lot of interesting areas with great variation and there is a lot of stuff to do. The post-game areas are great, you have a large area to explore with lots of strong trainers and wild Pokemon not seen during the main story. The graphics and the designs were excellent, once again an improvement of D/P, almost everything looked great. The music was also excellent, adding several new great tracks over what we already had from D/P. Platinum was innovative for being a third game just like Emerald, and I liked that. I still like it even today, it is my 4th favorite game in the whole series at the moment, and in my opinion, it was without any doubt the very best from when it was new up until the existence of B/W.
HG/SS on the other hand... I didn't like them. I had high expectations on them, but everything fell flat to the floor and was shattered. Apart from the expected and obvious improvements regarding graphics/physics/mechanics, I don't think they improved on the originals. G/S/C often gets credit for how new and innovative they were for their time as they introduced things like breeding, shiny Pokemon, held items, day and night, happiness and more. They should get credit for introducing these things and only for actually introducing them, which they deserve. But at the same time, they had a lot of problems. The level curve was terrible, the Pokemon distribution is screwed, the story was bad even by Pokemon standards, the "post-game" was boring as Kanto was a shadow of its former self with several places being removed, and Johto was very small as it lacked a proper post-game and relied on Kanto for its final bosses and what little post-game it had.
Then HG/SS happened, and they didn't improve on the originals regarding any of these things. They kept all the horrible flaws from the originals and did nothing to make up for it. They could have added new innovative things, but they didn't, instead just keeping things from Platinum like the Battle Frontier and the Wi-Fi areas without any changes. They also removed features like the Underground, Secret Bases and contests, while changing others for the worse like the Gym Leader rematches. I didn't care much for the things they actually introduced, Pokeathlon and Voltorb Flip are two of my least favorite minigames, I never bothered with the Shiny leaves but they felt like a rushed thing that was added in last minute for another Trainer Card upgrade. The following Pokemon feature is to me the single most overrated and useless feature in the entire series. The "amazing" touch screen did nothing, it was very slow and inefficient to use to the point that the menus in D/P/P were better despite not using the touch screen. Personally, I don't think Game Freak utilized the touch screen in a good way before B/W, which was less forced than HG/SS but more convenient. The story in HG/SS was bad like in the originals, the characters (both new and old) weren't as interesting as in the ones in Platinum. The story and the characters were marginally improved at best, which wasn't enough. The Pokemon distribution is still screwed with Johto Pokemon being uncommon even in their own region, while the means of obtaining some Pokemon in the post-game are just ridiculous. Johto and Kanto are both small regions without many points of interest and the games lack the fun post-game that Platinum had. I didn't like the graphics that much either, a lot of the designs for Pokemon sprites and other things like the grass in the overworld irked me. The music was fine at places, but could have been better for the most part.
Even worse than all of this, the problem with the lack of good training spots was never fixed from the originals. I find it more or less impossible to train in HG/SS as there is no efficient way to rematch trainers and the wild Pokemon are at too low levels throughout the entire game. To me, a game centered about training Pokemon is just not fun if there is no way to do actually do so. This was always my main problem with HG/SS, and will always be. With all of this said, there were a few things I liked about HG/SS like the Dowsing Machine, the breeding improvements and the large amount of legendaries to catch, but that's about it. It is nothing to write home about either as other games in the series has done these things equally good or better anyway. HG/SS lacked all forms of innovation and creativity which is a shame seeing as the originals often gets praised for all of the innovation and creativity they offered when they were new. Nostalgia doesn't save them either. If anything, I am thankful for HG/SS showing me that nostalgia doesn't make a game, gameplay and having fun while playing does.
There is a lot more that can be said on this subject, but I'll leave it with this. HG/SS could have been epic, but all the opportunities and potential they had to become so were wasted. Instead, they turned out to be a mediocre rehash of a highly overrated trio of games. Because of that, Platinum will forever by the superior and best 4th gen game to me.