The DS DEFINITELY is not the system with diversity. In my opinion, diversity in videogame consoles would be having the different genres spread as evenly as possible amongst your gaming library. I've only heard people name a couple of shooter games on the DS, and let's face it, they don't match up to the number of platformers or pet games anyways.
Discounting the PC, I'd go with...the PSP! It has tons of shooters like Tom Clancy, Killzone, SOCOM, and Star Wars Battlefront. With platforming it has Ratchet & Clank, Daxter, Patapon, and Loco Roco. For racers it has Need for Speed, Midnight Club, and Burnout. On the Adventure front it's lacking, but it still has Myst, Lego Indiana Jones, King Kong, and MediEVil Resurrection. On the fighting front (which I don't think it even exists on the DS) it has Tekken, WWE Smackdown, Mortal Kombat, and Naruto. With Sports games, it has a huge number of them with many that you probably wouldn't find on the DS. With Strategy games, I'd say it's definitely weaker than the DS. It still has games like Metal Gear Acid however, and a couple of Strategy RPGs. With Puzzle games it has Lumines, Lemmings, Echochrome, Crush, and a bunch of other games which I'd have to look up instead of using the database (the DS definitely wins in this category though).
I could run down a whole list, but the PSP managed to appeal to audiences who would like to play their console games on the go, which is why it got a lot of ports of shooters and some sports games. Not only that, but the PSP had humongous third party support at first which later dwindled (which allowed it to have a large back library of games), and the DS is the exact opposite (developers took a while to come but they did in huge numbers).
Not that the DS isn't diverse (it has lots of different games in tons of different genres) but its library is dominated by casual games, puzzle, or minigame titles whereas the PSP's library is a bit more even across the board.
