Context2D is slow and lacks a lot of features present in flash. It's not even really close.
If you're willing to put in the (large amount of) legwork, WebGL solves this, but it works on far fewer machines (even assuming up to date browsers) than flash -- well, if you discount mobile at least, not that WebGL on mobile works very well across the board.
Flash also was able to give you much better guarantees about things looking identical across browsers. This takes a lot more work when doing game UIs in HTML/CSS, to the point where my recommendation would be not to use HTML/CSS for games where this matters.
HTML5 audio element is very unreliable (it plays when it feels like) and limited. WebAudio theoretically should be better, but in practice you get pops and skips fairly frequently (depends on browser, etc).
There are other things too, but it's been a while since I did any work in flash/actionscript. Those are the ones that immediately come to mind.
Remember games like Farmville? They are all Flash-based. I don't think any of them have or even have plans to move over to HTML5 yet afaik. Flash made game development really easy with it's combination of AS and the wysiwyg interface for tweening and timeline motions. Currently, I don't think theres a definitive equivalent for HTML5 yet.
It's horsecrap. It's mostly just a case of companies with poor quality games that continue to be cash cows not wanting to put in the effort to port to HTML5 (because it wouldn't serve much purpose anyway, since their customer base are generally people who don't know anything about standards and probably instally any plugin they're prompted to install.)
Players are rapidly moving away from the web. The casual ones play their games on mobile and hard core ones are back on PC. Developers know this and that's why you can see a huge influx of Flash-like games on mobile and somewhat on PC (Steam Greenlight is full of those).
Can anyone elaborate on this? I can maybe understand premium video but games? What does the Flash runtime have that isn't mature yet in Web APIs?