Personally, I would recommend posting the youtube video directly on Facebook if you want it to play in the Facebook newsfeed. It might be possible to have the embedded video in your website also play directly in the newsfeed (though I’m not sure that it is), but even if it were it’s not going to be driving traffic to your website because the viewers of the video are never leaving Facebook. But it really depends on what your goal is:
If your goal is to get visitors onto your website, embed the video in a post and share it on Facebook. They’ll have to click through to your site to watch the video, but then they are visiting your site, which is what you’re really after.
If your goal is to get them to watch your video, share the video directly from youtube to Facebook so they can play it directly in the newsfeed. They won’t visit your site, but they will be more likely to watch your video because you’ve made it easier to do. It will also save you the effort of trying to figure out how to make an embedded video play automatically.
Hope that’s helpful.
