Linux is way better at some things but worse at others and depending on your needs and knowledge, a specific platform may suit you better. If your gf does nothing more but browse the web, read emails, chat here and there with friends, watch video online or offline on her computer, there's no reason why she couldn't use Linux just like my gf uses it and was in the past a Mac user until she saw that Linux could do everything she needs with ease and there's no need we spend a lot of $$$ to buy a Mac. As for actually jumping onto Linux, with ever platform switch, the user needs some time to get accustomed to. This is even true when you do Linux -> Windows. I, for example, as a long time Linux user will have problems using Windows and it will require time for me to dig around when I had to do something more than just click -> click -> install -> done
In this case, when you say "better", that word is very much relative. Better in what? In performance? Sure. In security? Sure. In ease of usage? depends stronly on the person who's using it and his familiarity with it., etc, etc
So, what I would suggest is setup a Linux environment for her. Make it as easy as possible by placing icons on her desktop of apps she uses the most (web browser, email client, etc) and let her use it regulary for some time. If she likes it and wants to continue to use it, then great. If not, then let her use her Mac and make Jobs even richer
Also, if she agrees to try it out, always be there to explain her what to do when she encounters a problem or doesn't know how to do a specific thing. When you do that, don't only show her how to do it but if you can, explain to her why it's done this way and why it works like that. You don't need to preach when explaining. A short explanation with good information will do
