they'll both run the same, with no differences besides the system differences in general.
either way, what system you have won't effect the game. end of story.
if this were a gen 4 game ( platinum, heart gold, soul silver, pearl, diamond ) then i would say ds lite for the ability to migrate from older games...
anyway! the system won't really effect the game in this situation, although the DSi is the better system in general if you're looking to buy ( which i doubt you are... )