The web approaches native, with asm.js and webgl. It is not just a document anymore.
Native approaches web, just look at what Apple, or Dropbox are doing(they use native code for giving you network capabilities).
Web software basically runs anywhere and doesn't have to be updated; it has minimal platform dependencies.
Native code, on the other hand, is a 25-year-long story of install/uninstall, sophisticated package/dependency management, chroot jails, and viruses.
I fear that, if web software continues its crawl out of the browser sandbox, we'll get all the disadvantages of native code (security exploits, dependency problems) without any of the advantages (speed, high-performance graphics)