If you're asking Linux users, the open-source platform is clearly superior to Windows 8 and 8.1 in terms of performance, security, appearance and customization features, but despite all of these, Windows 8.1 has clearly experienced a much faster adoption.
While it might be unfair to compare the adoption of the two platforms given that Windows 8.1 was offered as a free update to Windows 8, and Linux comes as a stand-alone platform, it's a well known fact that Microsoft's core modern operating system suffered from pretty low uptake figures in the first months on the market.
These figures provided by market researcher StatCounter show that back in October 2013, when Windows 8.1 hit the market, it was actually behind Linux in terms of adoption.
At that time, Linux had a market share of 1.1 percent, while Windows 8.1 was trailing behind with 0.32 percent. Things have changed significantly in just one month, so in November 2013, Windows 8.1 reached 1.18 percent, while Linux only increased its market share to 1.15 percent.
From this point on, Windows 8.1 adopted an ascending trend that increased the difference between this particular Windows version and Linux, so last month for example, it reached 6.17 percent market share, while Linux is only at 1.58 percent on the desktop world.
More specifically, here are the market share of each platform since October 2013:
October 2013
Windows 8.1 – 0.32 percent Linux – 1.1 percent
November 2013
Windows 8.1 – 1.18 percent Linux – 1.15 percent
December 2013
Windows 8.1 – 2.22 percent Linux – 1.13 percent
January 2014
Windows 8.1 – 3.19 percent Linux – 1.13 percent
February 2014
Windows 8.1 – 3.87 percent Linux – 1.14 percent
March 2014
Windows 8.1 – 4.48 percent Linux – 1.16 percent
April 2014
Windows 8.1 – 5.24 percent Linux – 1.34 percent
May 2014
Windows 8.1 – 6.17 percent Linux – 1.58 percent
As you most likely know, Windows 8.1 comes with quite a lot of improvements for Windows 8 users, including a Start button and options to boot directly to the desktop and thus ignore the Start screen. In fact, these two particular additions are probably the main catalyst of the fast Windows 8.1 adoption, as many of those who were disappointed with Windows 8 updated in order to improve the experience with the modern operating system.
Now it's obviously the turn of Windows 8.1 Update to boost adoption figures, but it remains to be seen how many users on Windows 8.1 actually deploy this new update.