There's already way too many articles that address the subject of which personal computer operating system (OS) is "better", Windows or GNU/Linux, but i figured i'd throw my own thoughts into the mix anyway. And let's first point out that Linux is not an operating system; Like the Windows NT kernel, Linux is also part of an OS called the kernel on top of which the desktop environment rides which is the graphic interface a general PC user interacts with. That said, i'll continue to misuse "Linux" as though it were both.
In asking the question, which is "better", we must first define what "better" is. Are we interested in comparing the two from a software perspective, a stability perspective, a security perspective, or a privacy perspective? Let's address all of them.
From a software perspective there is little doubt that there is far more software available for Windows OS's, however much of it, and probably the vast majority of it, is closed-source, proprietary software, as are the Windows OS's themselves, and this is a massive problem as we will soon realize.
From a stability perspective i think virtually all Linux users would disagree with my opinion that Windows XP and 7 were more stable than Linux-based OS's in my personal experience, but this is heavily dependent upon the user. I was a long-time Windows user starting with the dreaded Windows 95 version. In the latter years as Windows matured and, just as crucially, as i became far more selective regarding which software and updates i installed, i had virtually zero trouble with Windows XP or 7. If i experienced a system crash it was almost certainly a direct result of something i did, perhaps as an experiment. I could leave the system running for many days, weeks or months without rebooting. With every single Linux OS i tried there was always, and is always, something broken. That something is usually a part of the desktop environment or installed software however and not the Linux kernel. With regard to Linux, since that's what i use, stability is not quite as crucial to me as it may be to you. If stability is paramount and you're interested in Linux then you wouldn't be running rolling releases like Manjaro, Arch, etc., and instead would be looking closer at Debian or some other well-tested flavor of Linux.
From a security perspective i think Linux-based OS's are the clear winner, however there may be a caveat in that part of the reason for this is because there are fewer people using it and therefore fewer exploits are written for it. The Linux kernel, desktop environments, and the vast majority of software for the various flavors of GNU/Linux is open-source however and therefore any capable person can audit the code and submit patches, unlike the "security through obscurity" model of Windows and most of its software. Anyone who thinks that the black box security model is the better of the two should consider that huge swaths of the internet infrastructure, the world wide web, and a plethora of industrial controls and hardware devices such as routers, phones, watches, cameras, refrigerators, etc., are powered by Linux, not Windows. I'm not a security expert by any means however and so i will not elaborate further on this point.
"Arguing that you don't care about the right to privacy because you have nothing to hide is no different than saying you don't care about free speech because you have nothing to say." -- Edward Snowden
Privacy is the last perspective to be addressed and one of the most important to me. Privacy and proprietary software simply cannot coexist in my opinion. If privacy is at all important to you, and i think it should be even if you think you don't care about it, then Windows is entirely off the table and thus the question of which OS is "better" is completely irrelevant. Given the free-software ethic of the Linux community (and i mean 'free' as in open-source, not cost), Linux, its various desktop environments and nearly all of the software for it is far more respective of user privacy. It is also far less likely to contain malware and thus the need for anti-virus software, which is often malware in and of itself, is virtually eliminated.
Of course GNU/Linux-based systems are not the only ones to choose from for those concerned with any of the perspectives i addressed. For the casual computer user (email, web browsing, writing documents, etc.) i think FreeBSD is well worth considering. Though i've never used a BSD derivative i understand that they are very stable and secure, and that BSD offers a more consistent experience due to the more cohesive nature of the development process. Other than Linux and BSD however there is nothing else that comes to mind that is both mature and well-rounded enough for an average PC user. There is ReactOS which i mention more as a novelty item and because it's kind of an interesting project. ReactOS aims to be an open-source Windows compatible system, but unfortunately the development process is so slow that i suspect it will be obsolete before a stable release is ever realized.
For more on the subject of Linux and Windows, see A personal perspective: From Windows to Linux to Windows to Linux to...