I don't like to use the "It's free." line to convert people. It should be the reason people switch their operating system. Also, I think it only confuses the "Free speech, not free beer," aspect of the GNU license.
And, as much as I despise the insidiously malicious and monopolistic approach of the EULA and everything it stands for, there is sound reason and justification for purchasing software. (Whether it's the right price or not is another debate.)
Secondly, Linux isn't secure. at least, not like the common misnomer claims it to be. Many Linux distributions (Ubuntu, for instance.) have just as many security holes as Windows. (And for the record, Mint is a Unbuntu fork.) Certainly it's less likely to catch a virus or Trojan, but that's because there aren't any, not because it's less vulnerable. The only thing is more immune to out of the box is your run-of-the-mill malware.
However, Linux is much easier secure with some every day common sense practices; such that, a secured Linux computer is stronger than a secured Windows computer.
But, as I said, Linux's real power comes once you dive into the power of the CLI. I'm not going to bother with the real advanced stuff, but even your basic mundane tasks become so much easier once you learn the awesomeness of shell scripts. Things like making backups, scheduling tasks, sorting email, converting flac and wav files to mp3 or changing and mp3s sampling rate, converting bmps to jpgs or resizing them for TBBS thumbnails. This all can be done quickly and easily.
Now, a lot of that can be done with batch files in Windows. However, batch files are harder to write and are generally more cumbersome, aren't as inclusive and universal, and can't be fully integrated into the OS like scripts can--the last is great for tasks done on a daily basis.
But even if you want to move up to the desktop level, there are clear advantages. First and foremost are the options. You have the big three: KDE GNOME and XFCE, and then a whole bunch of smaller ones. I personally like Fluxbox. It's simple and really, really fast. And I adore window merging. Frankly, I think it's a bit funny that window merging isn't standard fare on all desktops these days.
But even within the options are options. They all have countless configuration choices, options, modifications, eye candy to mess around with to make your computer completely your own. Suffice it to say, you'd be hard-pressed to find two Linux desktops that are alike.
With that control comes functionality. People like to work their computers in different ways and being able to move things around to suit your own personal style really adds ease and efficiency.
Now compare this to the boring and pedestrian Windows and MacOS desktops. Where what you see is what you get. And you'll get it tomorrow and the next day, and the next. You don't like the placement of a menu, the behavior of the window, the icons, the window color and style? Tough. You're stuck with it anyway.
I know people who completely change their desktops around once or even twice a month. I think that's a bit excessive, but it's certainly the spice of life!
The same can be said for the file browsers. By default all the major ones (Konqueror, Nautilus, Thunar, Rox) are all more intuitive and functional than Explorer. But, again, if you don't like them, you can change them. They all have a plethora of options to fart around with to make your GUI life so much better.
Then there's the awesomeness of Package management. Let's face it, installing software on Windows is a painful chore. In Linux it's a few mouse clicks and your done. You can even install several programs at once.
But for me, the #1 thing Linux has over Windows is NO Registry! I have this working theory that like 70% of all the problems Windows users face are registry related. It is the bane of many Windows users existence and, for me at least, finally being free of it was a holy epiphany. God bless the /etc directory. But I digress.
While, Linux clearly has its fair share of faults and inconsistencies, I think the good far outweighs the bad. And, keep in mind that I only touched on a few specific things. There are many articles out there than can go into far greater detail than I can.