Diddy Kong Racing DS forced you to use a stylus to spin the tires or helicopter propeller or blow into the microphone to get a boost start from the race unlike the original where you just have to time it right. I don't have too much problems with it, but that is the most forced touch screen control I've ever experienced, and it's extremely intrusive to the entire game.
The Silver Coin missions were replaced by a touch-screen Balloon thing, although I actually prefer the touch-screen Balloon thing because I really hate Silver Coins, but both are pretty awful; one is too ridiculously difficult while the other is boring as hell; it peddles into both areas of unfun gameplay.
Character voices are butchered beyond all belief (what the hell did they do to Diddy Kong, Tiptup, Taj, and Drumstick's voices?) and some of the music in the game got replaced by inferior songs, with Pirate Lagoon's and Jungle Falls songs being replaced entirely (and Pirate Lagoon/Treasure Caves was one of my favorite tunes from the original Diddy Kong Racing).
You don't get character-specific colors for vehicles any more, you just use a slider that changes the hue of your car. It's a very lazy way to introduce custom colors in the game, rather than just make your vehicle white by default and pick colors from there using either color pickers or how Garry's Mod handled it when some objects use custom materials to custom-color some vehicles.
I did really love the vehicle customization system, though, but even so, only the speed upgrades are really useful and some upgrades are downright useless, such as upgrades that increase a plane's acceleration (all planes share the same acceleration no matter what). The rest can look nice but won't win you as much races as the speed increasing ones. What also makes it worse that you have to grind a lot of races endlessly for coins, that wasn't nice at all.
Oh and did I mention that Diddy Kong Racing DS got rid of barrel rolls and doing flips with planes? Those were fun to do in the original. Magic Codes are also gone as well, and I hate that too, because they were also fun to mess with. They also messed up controls for the plane and hovercraft but I think I eventually got used to those controls.
I also like how you can get special items such as Triple Missiles Surrounding you or Fake Coins. That's a plus I say for the game.
The level editor is so cheap and stupid that I'd rather not mention it. It may as well not be in the game.
The new tracks are all forgettable and bland. That's all I can say about them.
All of that being said, it's not a bad game since it's still mostly Diddy Kong Racing and I had fun with it. It's still a really botched port of a fine game, though.