As long as you update the Dstwo's firmware and EOS, it'll work perfectly on both.
That said, one thing I did notice especially with the homebrew, is how the DSi seems to add some kind of scanline effect... which seems to make those games even more accurately rendered. The scaler method the 3DS does for DS games does look good and smooth, true... but the scaline output seems unique to the DSi(XL), because I've not seen it on any of the other DS handhelds - not even the original DS. To me it seems strange because it's not like the DS/i should even know to do that, and yet the effect makes it almost convincingly like I'm playing the game on a CRT TV, and somehow more true-to-life.