Though Mac computers run on Unix, which is a Linux based operating system, there are still advantages to Linux over Mac.
The biggest factor for most people is the price. Since Linux is free, open source software, it does not cost anything. With a Mac, though, you will pay at least an extra $500, if not more. Though Macs use a Unix base for their operating system, they still charge a significant amount of money for the use of the software.
In a lot of cases, using a Linux operating system and using a mac are very similar. In other ways, they are very different. For example, updating software on a Mac can be frustrating and time consuming. You have to use the AppFresh installer every time you want to update a program. With Ubuntu, for example, everything stays up to date automatically. This is a huge factor for many people, who may not have the time to check frequently to see if there are updates to be made or not.
With Linux, all of the software that you will use is also going to be free. Since it is an open source software, you will be able to find many programs and pieces of software for free, that will serve the purposes you need. With a Mac, however, you may need to pay extra for these programs, as Macs are extremely proprietary.
Between a Mac and a Linux computer, the biggest difference is going to be the price. Macs are extremely proprietary, and can get very expensive. Using Linux software is free, and has about the same learning curve as a Mac does. They have about the same amount of computer security as well. If you are more worried about brand, you may want to stick with a Mac, but if you are looking for great functionality with a lower price tag, consider Linux.