No, you shouldn't care about performance, it should be as fast as native, these were concerns before but HTML5 is now getting more and more stable
Unity got an HTML5 export, and other big engines are also considering HTML5
and if you want desktop apps, you can export with NodeWebkit
the people talking about C2 as bad are probably people who tried it for 5 mins in beta and judged it from that experience
One last thing, C2 needs some big releases, it's not getting the attention it needs