I often see videos on Facebook and would like to have a more permanent link to them. I would like to find the same video on YouTube. Is there a straightforward way to find the YouTube version of a Facebook video?
Facebook and YouTube are two different services. While I expect a lot of people (corporations, etc.) would upload to both in order to maximize the potential audience, there's no guarantee that they would.
Assuming they have posted on both, there's no "link" between the two. One will have been uploaded in one place, the other at the other. Each service will give it it's own filename (if it even exposes the filename). At best, you can do a general web search for the title of the video or, if the description on both is the same you can search on that.
So, no, there is no straightforward way to find the YouTube version of a Facebook video, assuming one exists.