We went the second week in January and I loved it. A lot of the holiday decorations were still up, mainly the snow on the castle, n.o. square and wreaths around matterhorn/IASW and IASW holiday was still going. The lights were so pretty.
But it really doesn't matter when you go between both months. The weather is similar, attendance is similar and it's offseason so the offerings of shows/fireworks/parades and hours will be the similar both months. Just be sure to avoid MLK and Presidents day holidays. And keep in mind that Haunted Mansion will be down the beginning of Jan and back up around the middle of Jan and IASW goes down the middle of Jan and back up around the end of Jan to take down all of the holiday themeing. So if either of those are a must see for you, keep that in mind.