It's not as straightforward of a choice as it may seem. In theory Linux would be a better choice but there simply isn't the infrastructure or IT staffing in place to manage millions and millions of Linux desktops. I'm not saying it can't be done but for various reasons it hasn't been done and that's a major practical roadblock. Just from a staffing perspective alone if you hand millions of Linux desktops to life long Microsoftsies you're begging for disaster.
For sure, no question! There's a reason people choose Microsoft. My question was narrower, just the question on reliability (hence "all else being equal"). I don't think you can say that, leaving aside issues like this, that Windows is as or more reliable than Linux.
For instance, if you had to make deploy a mission critical server, assuming cost and other software was the same, would you choose Linux or Windows for reliability? Of course you would choose Linux.