Not OP, but imo the game library on the DS was better (the 3ds also had plenty of great games, just not as many). You do have to sift through an unusually large amount of shovelware to find the good stuff though, similar to the Wii.

Of course you can play DS games on 3ds, but you have to choose between blurry non integer scaling to full screen or crisp native but small with black borders. The games look better running at native res on the big screen of the DSi XL.

DSi are quite cheap and available compared to the 3DS which is a lot pricier. And dsi is quite sleek and simple (like the old iPods) compared to the 3ds line which got quite large and heavy (which a lot of People prefer)

In addition to the reasons others have stated, old games are designed with a D-pad in mind, not a circle pad/joystick, and the D-pad on the 3DS is in a slightly awkward position.

Personally the DS/i was just a bigger part of my life. The 3DS homebrew scene is a lot bigger but I still just love messing with the exact ds I used when I was in school.

If you are talking about DS games (so not emulated), they may need to be "AP-Patched".