ya, the Mini will be a lot more powerful, under warranty and telephone support, likely its smaller as well. The power usage is probably a draw between the finished systems.
Mac OS X vs. Linux is an interesting comparision. If you are running Linux already you are familiar with it. Mac OS X runs BSD as its foundation so most linux tools are precompiled for it and if not, can usually be made to work with about the same effort as you'd put forth on Linux to compile something.
The advantage is that you have ready access to much larger and commercially developed software selection on the Mac. The Mac market is probably an order of magnitude larger than the Linux market for home servers so you'll find it significantly easier to get the services you want up and running on the Mac. Well, unless you are a very experienced Linux guy. But in that case, why would you post here.
In short, the Mac is a lot simplier to admin but will likely have everything you'd need. If it didn't, you can pop the hood and get pretty much any Linux tool to work on it. Plus, there's easy access to great software and support, both commercial and free.
The Linux machine you'll spend a lot more of your time under the hood tinkering with stuff to get it the way you want to.
Which is the right choice for you is, well, up to you. I'd done it both ways and they both have their advantages. I'm at a point in my life where I'd prefer to spend a little money and get something where the software engineering has been done for me. So, I've got an apartment full of Macs and a server closet with a Mac Mini and a ReadyNAS Ultra 6 in it. But, as always, ymmv.
