Indeed, the reading system with more coverage of EPUB 3 is Readium, and it does not have 100% coverage of the EPUB 3 specs. (For example, the CSS 3 Speech module is not supported.) Unfortunately, you cannot install extensions in Chrome for iOS/Android, hence no Readium for iOS/Android.
Right now I work on Audio-eBooks (see my company web site to learn more), hence I have recently investigated the support of several Apps.
IDEAL Group Reader does a fairly good job, but has a lot of bugs when it comes to typographic aspects. The worst one is that it does not treat the newlines in the XHTML pages properly.
Lektz or Kobo do not support <audio>, not to mention Media Overlays. (Kobo has some "read aloud" function, but I guess it works only for their KEPUBs, and only if the device is connected to their streaming servers.)
Helicon Advanced EPUB3 Reader is atrocious w.r.t. typographical aspects.
iBooks does play <audio> and <video>, it has support for triggers and JS, but it does not support Media Overlays for reflowable books (and we all know this is just a "political" decision, to push their Fixed-Layout format).
To summarize: no app/reading system offers full EPUB 3 support right now.