DS lite is the older version. DSI just came out last spring.
DS lite plays all DS games and can also play gameboy advanced games and videos. My DS6 has this one.
DSi can can only pay DS games (no gameboy advanced) The additional features are pictures and you can edit and manipulate them. (VERY COOL FOR A KID AND MOM) and you can record voices. It also has some wifi capabilities. It is slightly different in size than the DS lite so some of the accessories are not compatable with each other. DS pens are a different size and not all cases will work. DS10 has this one.
Price for the DSi run around 169. You can find it on sale at times with extra games and such.
DS lite runs around 129 and less. Much more likely to find this around 100 if you watch for sales since it is the older model.