I think I've had an opportunity to play most handhelds, I definitely own a lot of them. I have a Gameboy Advance, Gameboy Advance SP, DS Lite, DSi, DSi XL, and the 3DS. Even though one of my favorite Sonic games is on the Gameboy Advance, I would have to say the DS is where I spent most of my time. I still have more DS games than 3DS games even though for a while I thought the 3DS was better than the DS.
One thing that I can say in VERY general terms, is that the DS has a better library of games than 3DS. I still enjoy many 3DS games like Mario Kart 7, Super Mario Land, Pilotwings 3D, Starfox 64 3D, etc. But games on the DS such as Super Mario 64 DS, Sonic Rush, Mario Kart DS, Mario Party DS, etc are higher in quality and fun than most games on the 3DS.
I also think that the location of the D-Pad for me is a bit annoying on the 3DS as you have to press it at an awkward angle. The DS I don't have to worry about that. I also think the location of the stylus is better in the DS and keeps the stylus from falling out of the system like in the 3DS. Additionally, the battery life on the DS is miles better than the 3DS. I can keep my DS closed over night without charging and it'll still have 3 hours of game time left when I wake up. I'll be lucky if my 3DS is blinking red by the time I wake up.
So what is y'all's favorite handheld video game system?