What are the differences between using whole wheat flour vs. all purpose flour in batter for frying?
Just as with kneading, stirring develops the gluten in the flour. over-mixing batter is a culinary no-no (fr. non-non). Batters are frequently rested in the refrigerator so the gluten can relax. Foods fried in batter that has been overworked and deprived of adequate rest is like a chef exposed to the same conditions–tough and tired.   

Whole wheat flour has considerable difficulty developing its gluten potential because when the outer coat (bran) is ground up and combined with the starchy endosperm, sharp particles of bran chop up the strands of gluten as they attempt to form. So the very quality that makes whole wheat flour such a 'pain' in the ass for bread making makes it highly useful for batters. 

Whole wheat has practically become my default flour. It's fine for dusting food articles on their way to the sauté pan, and for making roux. But bear in mind that you may need to use a little more roux than before to achieve a given degree of thickening. That's because the bran coat displaces a small portion of the starchy endosperm.