Both days have their special instrument. Purim the grogger, Chanykah the dreydel. Their use is indicative of the nature of the holiday.
Purim's grogger we hold from below to symbolize that the great Teshuva on the Jews provided an initiative from below which caused the divine initiative to bring about the miracle.
On Chanukah we use a dreydel which we hold from above to symbolize that the principle initiative for the miracle came from above, and our actions brought it to fruition.