Christmas in Japan is generally a commercial holiday. Expect lots of decorations around shopping streets. All Christmas decorations will get replaced on Dec 25th evening with New Year's ones.
On New Year's Eve there are no public events like fireworks. In major cities at midnight you can visit a Buddhist ceremony of ringing a temple bell (like in Chion-in Temple in Kyoto or Tennoji Temple in Osaka).
New Year on the other hand is a family holiday in Japan and a starting day for visits to shrines. Expect almost no one on the streets, but huge crowds at main shrines (like Inari Taisha or Yasaka Jinja in Kyoto).
In December and January "festivals of lights" will be held in Osaka and Kobe. Streets (trees, buildings, etc.) will be decorated by a large number of lights. For "Kobe Luminarie" prepare a few hours and expect a huge crowd (a few hours of waiting in line).
Some practical information:
Most places of interest to tourists (like museums or castles) will be closed between Dec 29th and Jan 3rd.
If you eat at restaurants, better be prepared for Dec 31st afternoon and Jan 1st. While there is a slight chance you might find an open "family restaurant" (not a family-owned restaurant, but a chain of restaurants of such class) somewhere around major station, but basically all places are closed (McDonald's and Burger King included). On Jan 2nd and 3rd many venues are closed too, but it is much easier to find a place to eat than on Jan 1st.
Public transport runs at night Dec 31-Jan 1st, but during the day trains will run on a holiday schedule (between Osaka and Kyoto they will run every 10 minutes anyway).
Private train companies running between Kobe-Osaka-Kyoto (Hankyu, Hanshin, Keihan) will offer 1-day passes at competitive prices for the first days of January.