My problem with HTML5 is that you have to use JavaScript on the client. Until browser vendors implement other languages I'll stick with native.
HTML5 is still the wild west, where anything goes. "jQuery spaghetti" is considered acceptable by many, and to convince developers who write in that style to provide structure to their application is asking them to do what often pushes them away from native development in the first place.
Once you build up a solid MVC (or similar) framework in which to develop your Javascript/HTML5-based applications, the differences between native and HTML5-based development seem pretty trivial to me, and a few syntactical differences between the languages used on the varying platforms are no more than a talking point.
It's the lack of choice that I find problematic.