If you have an old DS/DSi, I would absolutely play DS games on that. They look horrible on the 3DS because of the slightly higher (but not higher enough) resolution. By holding Start+Select (I think) when you start a DS game, it will display in the original resolution, but then you get bigger borders around the screens.

No... they don't... 

The black bars on the side of the top screen are so that the sizes of the top and bottom screen match, since unlike the DS, the 3DS screens are not symmetrical.  But the game is being stretched to fill in the rest of the screen.

There shouldn't be any difference compared to the 3DS or 2DS, since the game will be stretched anyways

Maybe not the same resolution then, but it barely stretches them. The bottom screen is almost exactly the same size as it was on the original DS and DS Lite (at least on the normal 3DS and 2DS), so the black bars also make it almost the same resolution as the old DS. Certainly not very noticeable. At most, an extra 0.2 inches.

For me, there has never been a noticeable difference when playing DS games on 3DS, apart from the screen on my 3DS XL being larger than the one on my DSLite.

I still have my DS lite and I am not replacing it, it's one of the best handheld experiences I had

It's a pretty noticeable difference to me, to the point where I usually play in original resolution mode.