Windows has made a lot of advancements, but the picture is not clear cut.
Performance: Graphics driver stack and utilization Windows is ahead by a wide margin. Otherwise Linux usually wins (though some debate can be had about scheduling behaviors). For reference, look at the Top500 list and count the Windows deployments versus Linux.
Security: This really is more subjective than objective in many ways. Windows let's you *think* you are logged in as admin without actually giving admin in a pretty sophisticated way. Given the common use case of desktop users using just one account as 'admin', this is probably one of the most important facets. Additionally the ability to hold multiple security contexts without having distinct processes enables applications to take advantage of OS privilege enforcement in a more efficient manner. On the flipside, Linux has more advanced namespace manipulation and enriched mandatory access control. There is much better framework for hard enforcement of very fine grained things in Linux.
Stability: At this point things are fairly even. MS gets a nod for more resilient graphics stack, but I'd say the quality of third party drivers is frequently lower in Windows than Linux. I get more crashes on a modern Windows system than a Linux system, but I don't think MS is to blame anymore directly. If Linux were more popular and third parties did the same BS they do in Windows, Linux would probably suffer just as badly. In this way, the GPL I think has helped Linux as a kernel greatly.