There is no shortage of articles on the Internet about the cross-compatibility of HTML5. The bigger question at hand is not whether HTML5 is compatible on platforms, but whether it works well on all platforms. Obviously, with the sheer amount of devices and operating systems that the language supports, there will be some differences in terms of speed with regard to how the code is processed, but it will be easier to find places that do it well than places that don't.
The problem with attempting to be a strong language for all different types of operating systems it that HTML5 widgets cannot be content with simply being good across a variety of systems - they must be better than any system's individual most well-optimized code. HTML5 needs to be the reigning champion across many different systems. In order to figure out whether or not these devices' interactions with HTML5 are actually that strong, some investigative reporting is necessary. Luckily, if there's anything the development community loves more than development, it's stress-testing other people's applications.
Tests performed on HTML5
While it is at this point a given that it is easy to build cross-platform developments with HTML5, as the people at WhaTech pointed out, developers should now look to make sure that HTML5 is an efficient language in their platform of choice. As more support comes out, HTML5 should become stronger across all areas, but specific improvements can always be made. Like other major languages that have preceded it, HTML5 will only grow stronger as it is more overwhelmingly adopted and has more systems optimized to make use of its specific capabilities and specialties.