HTML 5 has prevailing problems, for example with sound:
http://en.wikipedia.org/wiki/HTML5_Audio
"The result is that for a website to guarantee HTML5 audio for all users, it has to make two formats available, often Vorbis, as used on Wikimedia sites, and MP3 or AAC."
Since every browser vendor implements HTML5 as he likes, using different codecs and formats, it is pain for the content providers to ensure everything looks and sounds as intended in every browser.
Flash was a closed platform provided by a single company.