I've used them all. To me, Video JS and Media Element function the same. I prefer Video JS because it seemed easier. It depends if you want to use javascript or not. True HTML5 video, as presented here, has no javascript. I guess it depends if you want to go javascript and what scale of video production are you doing - massive blogging or a few commercial videos here and there.

If you are going blogging, save yourself the trouble and use vimeo or youtube. If you are doing a few commercial videos, then html5 would be suffice.

True, HTML5 video doesn't need additional javascript in browsers that fully support it, but there's a few reasons you'd want to use either of those libs.

- Fallback to a Flash player for IE <9
- Device/Browser bugs - iOS 3, Android 2, and certain browsers have serious playback bugs that can be fixed with javascript
- Consistent player chrome + features between browsers

Cheers,
-heff (video.js)

@Heff
Good points. Video JS.

*vlog or blogging* - use a third party because your cost will be out the window - especially if your site becomes popular. You can do youtube that integrates with JWplayer (recommended); this way you have a detailed analytic suite and other great add-ons from the community. Or, Vimeo - which I'm doing research on their paid version. If you go this route, take a look at your vision, values, message and plan to see which medium is a best match.

Commercial (products or sales video) - use Video JS. I prefer uploading the video to Amazon s3 and using cloudfront to stream the video. JWplayer has great instructions in their tutorials for making this happen.