You can not equal or elevate either Christmas of Hanukkah, the religious observance.
What you are talking about is the Season. The Season is not a religious observance, it's a commercial social experience.
In American culture, the Season has come to incorporate both holidays because they are similar is their gift giving nature.
But the days you actullay celebrate Christmas Eve and Christmas(always at the same time) or that Jews celebrate Hanukkah religiously should not be equal or equivalent to either group.
Excuse my typos, anytime. I post to FR and do other things simultaneously and errors are a consequence.