For those who tl;dr:
Windows is cheap, semi confusing, not so secure, best compatibility.
Linux is free, confusing, good security, and least compatibility.
Mac is expensive, good security, and semi compatibility.
I run all 3. I fix all 3. All 3 have perks. All 3 have downsides.
Now, for the breakdown I am going to assume we are focusing on the DESKTOP environment world, as the SERVER environment world is a whole different topic, and I could get into that too if you like.
Note: For discussion sake, I am not including notations about Virtual Machines and Dual Booting. Yes, I am aware Mac has Boot camp. However, nearly all of these products have this option in one way or another to support the others.
Break down:
--Windows--
Hardware: Windows is compatible with virtually all x86-based hardware out there.
Software: Due to Window's popularity, software support is high in this regard.
Security (Exploit): The Vista/7 UAC major overhaul did help windows hardening, however they are putting band aids all over a product that was never designed with security as focus. Unfortunately, it is difficult to understand how secure Windows truly is in comparison to other operating systems due to the fact Windows will naturally have the most known vulnerabilities, simply from the popularity of their product and attraction it would get from malicious users.
--Linux--
Hardware: Compatible with virtually all hardware.
Software: Since linux is a kernel with a collection of packages varying by distribution, this question is a confusing one. Due to it's open nature, there are many compatible solutions with linux for desktop users. If we focus on code written exclusively for linux, there are not many that have not found it's way to other X-11 based platforms (such as OSx or other Unix-termed OS's), so even harder to isolate. Wine has done a good effort to support Win32 binaries and hive emulation, so it's support can be some what surprising at times.
Security: Linux is difficult to gauge security due to there being so many distributions and packages available to the product, plus it's a kernel, while the other two are OS's. Most distributions enforce security by default, and they tend to keep the user in a limited access mode without escalation annoyances too much for daily work. Linux is based on an architecture that has ran the backbone of the internet for many years, however, so it is easy to argue towards a stronger security than most, especially with it's built in permissions. Linux also is good about distributing updates and users tend to do them regularly.
--Mac (OSx)--
Hardware: OSx uses an x86 platform specifically catered to their operating system, however does not differ in any significant way to other x86 systems, minus the EFI boot loader and very compartmentalized "logic boards" as opposed to motherboards, and lastly file allocation table type (GPT is not significantly improved vs others however). Some may argue the engineering quality of mac hardware, however, being an apple certified tech, I know that many of their products are known for glaring defects (which should be expected with how custom they go in aesthetics). Fortunately, they tend to be good about replacement on early caught warranty-covered defects, however that is not always the case for older products.
Software: Mac has one advantage with their closed off system for products. This tends to create a higher standard of software development, especially with their specialized XCode IDE. This can be a double edged sword, however, because running Mac exclusively locks you in to certain choices, and not a lot of variety otherwise. They have relative good compatibility with linux-based products, too, so can be argued to the same degree as linux has for compatibility.
Security: Mac has done a good job at keeping security relatively high on the OS level. The discussion about linux can be noted here too, as OSx (Darwin) is heavily based on the BSD/Unix systems.
