This story is different because browsers now agree that compatibility is important.
Consider, for instance, IE9's "same markup" marketing. That's really an indication of the current mentality.
In second place, HTML5 is incredibly backwards-compatible. <input type="number">
will render like a plain text input field on IE6(and, as a result, graceful degradation is made easy)
Of course, people are still using many old browsers, but none of them have IE6-like market shares, so they can't really be compared. Also, the upgrade cycles for browsers seem to be shorter than they were in the early post-IE6 age.
I currently think that IEs < 9 are the most likely to become modern age IE6. For Chrome, its upgrade cycle makes it very unlikely. Not sure how Safari and Opera compare, but they definitively don't have massive market share, so they really have no chance of becoming IE6-like(I am not considering the mobile world).
As for Firefox, it also includes free and simple upgrades, making me think that Firefox users will upgrade soon enough to the new version when it becomes available.
That leaves us with IE9 with no XP support, meaning that most XP users will use IE <= 8 until they switch OS.
EDIT:
One more thing I really should mention: The spec of HTML5 takes compatibility across web browsers VERY seriously. I believe that will help reduce the incompatibility risks(although that certainly won't make Internet Explorer support WebGL, nor make Firefox support Web SQL).