Can't say I know, but after doing some searching, I have found that Youtube itself has been fighting against people embedding higher quality videos. Some elements that used to work when added to the video link have recently stopped working. It's possible that the quality degradation and the installation of W3TC are coincidence.
Have a new video put into the website and pay close attention to the URL and other data as it goes in. Then check the page that is processed and sent to the browser. If the URl or other data has changed, then at least we know the issue might be with WP or W3TC. If not, the issue is most likely with Youtube.
Other than that, it seems unlikely that video quality should be affected. Youtube videos aren't stored locally and aren't cached. The only thing I can think W3TC could affect is the link or less likely some of the other details included with the embed.