Just to add.
There are some differences (noticeable) while you run Pokémon White/Black in DSi mode. The battery indicator in the lower screen don´t have 2 bars (DS mode, frankly speaking about green led while full charge, and red led while in low level charge), but instead will have 3 (DSi software uses 3 bars which tell your current battery charge more accurately.
Besides of camera function, and the ability to connect to Dream world & GTS with a WPA set router.
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This is just a personal statement, but B/W in DS mode will run a bit "stretched" on a DSi, it´s noticeable because characters (of overmap) will look more pixelated, and in battles the nearest pokemon (yours) seems horribly pixelated, while in DSi mode there´s some sort of "aspect ratio" kept at screens, and also, the nearest pokemon in battles will look more "drawn" rather than pixelated.
All this using both a flashcard & a legit Pokémon White cart in a DSi (not xl).