Held From Below

On Chanuka their teshuva was not complete, for they were aroused from Above rather than engaging in proper teshuva, and that is why one holds the dreidel from above. On Purim, on the other hand, the teshuva came from being aroused below, by fasting and lamentation, sackcloth and ashes, and that is why the gragger is held from below.

(Ta'amei Minhagim I, 99)