Well the grey card is designed for exposure and not necessarily color and may not give you the best colors while a good white card is supposed to be color neutral so as to get the best possible representation of the current "white" light. I usually shoot both sides when I'm prepping to shoot photos or video so I can color balance and recurve the exposure later - the grey card for the proper midtones and the white card for highlights. For the best color, you can get dslr color balance cards that do wonders for setting the best possible colors.
Not all grey cards are the same. Most of them are 18% grey, a few are 13% grey, and modern DSLR cameras do not have an exposure range corresponding to either (something like 12% according to my calculations).