Don't upload if not necessary, really to help speed up site. Embedding videos is easier. YouTube videos specifically are SEO BEASTS right now because they are owned by Google and just rank really well in general and are good back links to your site, from YouTube videos, and are good to embed on your page.

YouTube embeds all the way.

Google owns YouTube and to me it sounds very logical that

google adjust the algorythm so the website with the youtube embed ranks better.

I go with YouTube. The reason is because YouTube belongs to Google.I've seen a lot of great results from putting a YouTube video on your page that is relevant to your content.

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no difference

Will there be a difference in ranking if my website uses Youtube embeds over Amazon S3? Also I heard that uploading the video directly to the website may be better?

10 points for a straight answer, thanks.