The reason everyone asumes HTML5 apps can't work on mobile is because how awful UIWebView is on iOS. Apple really need to explain how limiting JavaScript speed in WebView makes it anymore more secure.
The good news is, that with Remote View Controllers in iOS 6, we may get Nitro'ed UIWebViews in a separate process (like how home screen apps work) that have their own secure set of executable pages. See: http://oleb.net/blog/2012/10/remote-view-controllers-in-ios-...
As bad as UIWebView is, it somehow manages to be the best webview out of any mobile OS.[1]
[1] as for BB10, I'll believe it when I see it.
I sure hope the downvotes aren't for saying that iOS's uiwebview is the best one we've got. Android web views mean using the android browser rendering engine, which is terrible. It might not be intentionally crippled like apple's is, but it is less capable to begin with.
On mobile there is no question whatsoever that CSS3 animations are much better. The big issues tend to be regarding 3d stacking contexts. You can end up with strange artifacts, z-index breaking transforms, and sometimes downright wrong positioning. Also GPU accelerated elements can sometimes come out blurred. jQuery animations fix this but perform much worse.
On desktop it really depends. Browser compliance is an issue a lot of the time. You can actually slow down a 2d transition by using translate3d or any other GPU accelerated value. GPU acceleration hasn't had all its kinks worked out yet in browsers but its very likely that CSS3 transitions will be miles ahead for regular use cases in the future. I'm not saying that CSS3 transitions are worse, just that they are not better all of the time (only most of the time).