To commemorate Chanukah our chachomim instituted the mitzvos of l’hodos u’l’hallel (to give thanks and praise to Hashem) and to commemorate Purim they instituted mitzvos to eat, drink and be merry.
Why do we give thanks and praise on Chanukah, and mark Purim by eating, drinking and merrymaking?
On Purim, Haman wanted to attacked us physically, so we celebrate in a physical manner. Chanukah was an attack on our spirituality, so we celebrate our deliverance in a more spiritual way.
—The Levush
Why don’t we celebrate Chanukah for nine days, adding an extra day for doubt like Pesach and Sukkos?
The first reason is that Chanukah is d’rabbonon, so the the rabbonim didn’t feel the need to be so strict.
The second reason is in celebration that we could still perform the mitzvah of bris milah (on the 8th day), which the Greeks tried to obliterate.
Every year on Chanukah a new light and energy come down to the world. אור חדש has a numerical value of 219 and להדלק נר חנוכה has a numerical value of 218.
All that’s needed is one more, you, to bring down that extra light.
—Bnei Yissachar
Why do we kindle the menorah in the doorway of our homes?
It is because Chanukah is the opening to the geulah.
—Sfas Emes