Browser version only matters if you're looking at or developing cutting-edge web technologies.
For any other users in 99.99% of cases it doesn't matter.
Devs do need to know this stuff, and act accordingly. But if the right strategies are used every visitor can get a usable site and not have to worry about if they're using SuperBroswer v13.2.4.094 alpha 3 nightly 6
Since the launch of Chrome, the browsers release cycles has been so quick that it is hard to keep a log of it. Thanks to the seamless upgrade, there is no need to.
It is amazing how it took more than 5 years for Firefox to go v1 to v3; but it took just over couple years from v3 to v15.
It only matters, when I want to view something like the newest WebGL demo.
Additionally, it matters, if a version update breaks a plugin, but this is not specific to a certain version number.