G0LD makes a very good point with the DS lite having the Dual-sot feature for migrating!
One difference between DS lite and the DSi is that the DSi has like a half inch larger screen, and you can change its screen brightness MUCH more easily.
Also, performance wise, the DSi is better; (67.028 MHz ARM9 and vs. 133 MHz ARM 9 processor).
So technically, the games will run better on a DSi, which means less freezing and less lag (if any!).
Although it really isn't all that different.