Jan 19, 2020 - 5:21 PM
We were at both last October, so keep in mind the weather will be considerably different in January.
Pilatus - More infrastructure at the top, two hotels, restaurant, large indoor snack bar/lounge area with big windows, expansive outdoor plaza, but limited walking trails/paths although the short tunnel walk around the peak is quite impressive (not sure its open if the winter weather is bad). It is also an uphill hike from the Kriens bus stop to the gondola station, short but uphill nonetheless.
Titlis - Much more oriented to outdoor winter activities, walking on the snow, a short pedestrian suspension bridge (lots people taking selfies there, and it sways a bit). More of that "in the Alps" feel to it, and it is about 3500' higher than Pilatus. Also a more scenic train ride from Lucerne to the base than the bus ride in Lucerne to the base of Pilatus.
Either way, dress warm and be sure to check the weather forecast and mountaintop web cams before you go. No sense doing either if the weather is bad. If the weather is bad, touring old town Zurich or Lucerne would be a better way to kill time.