While Netflix and Disney have yet to release official streaming figures for The Witcher and The Mandalorian respectively, a 3rd party tracking firm, Parrot Analytics, which keeps track of tv show's "demand expressions", a globally standardized TV measurement unit to reflect the desire, engagement, and viewership of a series, has announced their data for the week of December 22-28. According to their data, The Witcher, in it's 2nd week since release and first full 7 day week since release, surpassed The Mandalorian and Stranger Things to become the most in demand tv show. The previous week, from December 15-21, The Witcher ranked 3rd place, behind The Mandalorian at #2 and Stranger Things at #1. Stranger Things had been on a 21 week streak of 1st place finishes based on Parrot Analytics data before being dethroned by The Witcher.
It is worth noting however, that The Mandalorian episode 7 premiered on December 18th, 4 days before this tracking week began, while episode 8 premiered on December 28th, the last day of this tracking week, which leaves most of this tracking week on a large gap between 2 episodes of The Mandalorian. It is also worth noting that Disney+ is pretty much available in the US only, while Netflix is available worldwide, though The Witcher also came in first based on US only data.
Netflix also released their top 10 shows of 2019 list this week, which is believed to be based on the number of people that watched at least 2 minutes of a show within it's first 28 days on Netflix. The Witcher made that list at #2 in the US, only behind Stranger Things, and it beat Stranger Things in the UK and Australia. The Witcher also made #6 on the combined top 10 show+movie list. It is believed that Netflix used projected views for the first 28 days of The Witcher based on the data they do have, since the show hasn't been out for 28 days yet.