I know its an old thread, but I will answer this for future reference:
The analog stick works like a surrogate d-pad. You can use either, and if the DS game you are playing is able to do 8 way movement (like Super Mario 64), the analog will feel natural, but if the game is only able to do 4 way movement (like the Pokemon games), the analog will feel just a bit stiff.
BUT in these Zelda games you move Link with the touch screen, not with the d-pad, then the analog won't move Link. It will only do what the D-Pad does in the game (in this case, pulling down the map)