Main difference: it does not degrade gracefully. It just doesn't work without JavaScript activated.
Who cares, really? The percentage of people who purposefully break their browsers isn't worth catering to.
Accessibility. Is there really any reason why a questions/answer site with voting can't provide noscript tags?
Refactoring ours to deal with that, so not trying to throw stones.
EDIT: I understand mythz's comment about being a play project. i'm just responding to the 'why break your browser' sentiment.
Because making two versions of the site is twice as much work?
This demo doesn't let you link to (or bookmark) a page or open questions in new tabs. For an app like Gmail that probably doesn't matter, but for something like this I'd say it's pretty crucial functionality to be missing.
Progressive enhancement where you add JS to improve the experience is a much better approach. That way you get all the basic functionality for free instead of trying to retrofit it onto the ajaxy app.
Now that you can manipulate the address bar with pushState [1] you can even make these enhancements completely transparent.
[1] https://developer.mozilla.org/en/DOM/Manipulating_the_browse...
Is there a way to make it degrade gracefully? The problem I see is that you can't have the JS and non-JS parts have the same URLs. The JS part will have urls like thesite.com/#question123, whereas the non-JS site will have urls like thesite.com/question123. So now you have two urls for each page, giving problems with search engines (and I think search engines will consider thesite.com/#x the same url as thesite.com/#y, and only load one of them).