This post is inspired by Tim O'Reilly's The State of the Internet Operating System, only 6 months late.
Can a Web Browser be as Full Featured as an Operating System?
No. It's silly from a technical standpoint to confuse the job of the browser with the role of the OS. Browsers render html documents and interpret javascript. An OS handles all the hardware intricacies, drivers, low level language compilation, and specific interaction with virtual machines. The OS handles resource allocation, security logs, regular updates and patches. clearly there is a difference in designed function between web browsers and operating systems.
Looking closely at what a browser is designed to do, I defer to documentation of both HTTP 1.0/1.1, and HTML standards. Browsers are required supposed to support at minimum the features described in the standard. The most popular web browser in the world (IE 7?) has numerous exceptions to how it interprets markup language, causing frustration for designers and developers alike. But it's not entirely to blame, despite it's quirky behavior.
On top of this, attractive features that will be in future standards (HTML5) like curved corners or dynamic gradients are supported in multiple browsers, but have different tags and interfaces. Native video support is in a variety of browsers (HTML5), and has been accessible through the Flash extension for several years. Powerful 3D graphics libraries are just now becoming available through other extensions.
Will browsers of the future compete on the quality of embedded game and 3D physics engines?
Most recently, I covered my first impression of Minecraft. Along with Quake 2's port to the browser, it's a perfect example of a browser based, interactive 3D graphical world. The technologies used include Java and Open GL and are referenced in the post. There's an opportunity for video hardware developers to trail blaze towards advanced browser rendering capabilities. Key resource investments focused on improving efficiency for open graphics libraries, will be a competitive advantage in both the explosive social gaming market, and other advanced graphics applications.
Conclusion
While browsers aren't operating systems, they will likely serve as the dominant application market over the coming decade.