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It works pretty well though it lacks a download file button for those who want to give the option for people to download their MP3 files, still it is nice that WordPress now put a build in MP3 player so you can add audio files.
If you do podcasting however, there is still so many advantages to use Blubrry Powerpress, SoundCloud, Libsyn or another service that can not only create feeds, and/or social communities around your audio files, but also allows you to not use your web server hosting resources to serve the files in the case of SoundCloud and Libsyn it is served from their cloud instead of consuming web hosting resources to playback the audio files. Blubrry Powerpress has a great auto syndicate your podcasts to iTunes which works well and was tested for my Audio poetry two years ago and still is in use there.
The same for the video embed player, I prefer to have my videos on YouTube and embedded so I can leverage the social following, subscriptions…etc.
Have you used the HTML 5 player embed in WordPress 3.6 yet, and what do you think of it?