No, you don't get anything extra, and you might even have less features on a DSi, because of the removal of the dual slot mode. BUT, I have a DSi and a Lite to compare, and the quality of a DSi is much, much better than a regular DS/Lite (in my opinion anyway). It seems like the definition is much better, the screen is somewhat bigger and the backlight is a bit stronger. I seem to like the smoother gameplay that the DSi offers.
But if you want to use the dual slot feature, then I suggest you stick with your Lite, or keep both DS's at your side, which is what I do.