Since most HTML5 platforms these days render on the GPU (including Safari for iOS), porting to a native app will probably not get you extra render performance. It will still render the same way on the GPU. (WebGL just helps reduce the CPU burden of rendering.)
Logic performance is all that's improved by native tech. On desktop usually the logic accounts for 20% of the frame time, and the rendering accounts for the rest. On mobile it's tighter because of a more limited CPU budget, but a well-designed game should be able to get by. Native mobile game developers probably have deeper technical knowledge of the platform, and use very clever design and tricks to ensure they can make the most of the limited computational resources available. I think part of the problem with C2 is it makes it so easy to give a mobile device too much to handle.
Think about render performance again. Consider leaving 'clear background' on, then creating two fullscreen tiled backgrounds laid over each other (or a screen-sized sprite for example). You have already reached 100% of the pixel pushing budget of some mobile GPUs (which can only write to every pixel on screen 3 times in 16 ms). A native app developer would know not to do that; set 'clear background' off, use one opaque tiled background to give the background texture (perhaps with an effect or artwork "baked in" to the image), and start building the game off that. Then you're starting with 66% of the GPU pixel pushing budget free, rather than 0%. I know this type of thing happens, because I have been sent .capx projects with users saying "it's horribly slow, C2 sucks" or whatever, and they've done something like overlay 3 full-screen sprites right off the bat, so a simple game seemingly runs slow. You just can't design games for mobile like that, not even with native technology.
I think another big part of it is bad methodology: users create an awesome game using tonnes of effects that runs perfectly on a desktop, and then suddenly find it works slowly on a mobile. What you need to do is use preview-on-LAN right from the start, literally after clicking 'new project', throw in the FPS and object count in a text object, and preview exclusively on mobile while keeping an eye on the FPS. If the FPS takes a dive after a change, backtrack and find a more efficient way to handle it. Your desktop computer could literally be 100x faster than your mobile, no exaggeration - so it's just not sensible to design mobile games any other way. I get the feeling not too many people take that approach!
HTML5 tech is still developing. I would encourage you to try Chrome Beta for Android, with WebGL enabled in chrome://flags. It's by far the best I've seen HTML5 games running on mobile. And I think it's clear Google's intent is to eventually have WebGL on by default and shipped with the stable version of Chrome (that is now pre-installed on new Androids). I think that's the best indication of what the future of HTML5 on mobile is.