The main threat to your privacy induced by BitTorrent lies in your IP address being stored in the instance's BitTorrent tracker as long as you download or watch the video.
The recently added video<x id="START_LINK"/><x id="INTERPOLATION"/><x id="CLOSE_LINK"/> has been <x id="START_LINK_1"/>automatically blocked<x id="CLOSE_LINK"/>
the sharing system used for this video implies that some technical information about your system (such as a public IP address) can be sent to other peers.
The threats to privacy with YouTube are different from PeerTube's. In YouTube's case, the platform gathers a huge amount of your personal information (not only your IP) to analyze them and track you. Moreover, YouTube is owned by Google/Alphabet, a company that tracks you across many websites (via AdSense or Google Analytics).
The worst-case scenario of an average person spying on their friends is quite unlikely. There are much more effective ways to get that kind of information.