HTML5 is more compatible with newer devices like iPhones, iPads, and Android Tablets some of which don't do flash yet. It also means people who don't have flash installed for any number of security reasons can still use and see the videos. Overall HTML5 is a better technology for your users.
However as an admin there is a small tradeoff on SEO from what I've read. IFRAMES don't count towards your SEO so a URL that would be on your page from Flash embedding, perhaps with keywords in the URL or the embed code itself will not be present in the IFRAME/HTML5 code.
Personally I use HTML5 whenever possible as I'd rather keep the people currently on my site happy more than the small hit I might take with SEO.
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