>>43669868DP is by far the worst offender; its Surf speed is as excruciatingly slow as that game's walk speed, and every single action during battle has useless delays around and in between.
They rectified the Surf speed and most of the in-battle delays in Platinum and HGSS, but battles still run much slower than other generations.
Saving is a different issue; it also takes much longer in Gen 4 as the ratio between the cartridge write speeds and the amount of data to be saved is by far the worst in the series, and the developers didn't do a perfect job at requiring the game to only save unchanged data. Platinum is worse than HGSS at this for sure; in particular, if the status of the PC box has been changed, the game will display a "Saving a lot of data..." message and take a very long time. I've heard Platinum actually regressed from DP at this, but I've never played DP, so I can't confirm.
>Pt and HGSS on 3DS hardware dont feel slow at all, saves in a few seconds etc.This is just you; the save speeds are limited by the cards, not the consoles, and the 3DS basically has a DS inside it that runs the games in exactly the same way.
Try Gen 5 for a comparison; despite being on the same hardware, battles and saving are much faster.