new 3DS:
Better CPU (Quad-core, original had a Dual-core).
Better coprocessor (4x, compared to 2x of the original).
Double the RAM (256MB, compared to 128MB of the original).
Overall just a faster and smoother experience, even more so if you install homebrew (check gbatemp), which also allows you to utilise the faster CPU with older 3DS games (FPS improvements with Pokemon, anyone?). As well as emulators (which perform better on the n3DS).
Sadly Nintendo didn't give you the option of utilising the new specs on old 3DS games, which is why I mentioned homebrew.