This isn't about debating which. I used a question as a title for the sake of answering why my family chose Chanukah. Believe it or not, not everyone who does Chanukah does so because it is a "Jewish" Holiday/Festival. It's not a commanded Feast like Tabernacles (Sukkot), Passover (Pesach), and Pentecost (Shavuot). The reason Judaica (Orthodox to Progressive to Messianic to Hebrew Roots) choose Chanukah is because of its Jewish/Hebraic cultural beginning. Most, at least, in those circles who choose it over Christmas, are doing so for this reason, but not all are. [They] celebrate the retaking of the Temple by the Maccabbees and the "Chanukah Miracle" of a single day's oil lasting 8 days. To be honest that miracle can't be verified by any relevant source. But that's not why my family chooses to celebrate Chanukah over Christmas anyways. I'm neither for nor against the "Chanukah Miracle". It's simply not relevant to me. The story of Messiah's birth in Luke 2 is why I choose Chanukah. The story gives us all the clues we need, to understand what time of year it was. The census of Rome would have been done during a time when it was easiest to get all of the MEN counted and determine the size of their families and their income source. Clearly the easiest time would have been during a COMMANDED Feast. Only 1 of the 3 commanded Feasts fits the bill because of what we see with the shepherds. They were on a hillside, which means they'd climbed in elevation away from the typical pasturland. Customarily this was done during Fall into Winter in order to preserve what pasturland they had below for the cold months ahead. It was also because the "former rain" that came as part of their twice a year rainy seasons. It would create quite a deluge of water in the lower lands and having their flock trampling on it would be a surefire way of killing the grasses off for months to come, a bad strategy when you need to be able to feed them close to home because of the unpredictable nature of winter weather, especially in higher elevations.