Buy a Mac, don't buy a Mac. There's a thousand reasons to do either. Ultimately it's personal choice. I've used PC's since the days of DOS and build, service and support PC's as part of my working life and have done for the past 23 years.
About 5 years ago I decided to switch to Mac at home and I can honestly say that I can't ever imagine buying or building a PC for home ever again. Does my Mac do stuff my PC's can't do? No, of course not but my productivity has gone through the roof using a Mac and it's just such a huge pleasure to use which is something I could never say about Windows. But none of these are reasons why YOU should buy a Mac only YOU can decide that.
If you do decide to buy a Mac, Aperture is a joy to use and as I've said in other threads on here recently, there are parts of Aperture that stomp all over LR. That said when LR3 came out I finally made the switch from Aperture to LR because the difference had become so small but there were a couple of killer features in LR3/4/5 that I wouldn't want to be without.
The other thing to remember with Aperture is that it is a bit sluggish compared to LR. On an low spec machine you will get the dreaded beach ball if you have a large library. On a mid spec machine you may get it occasionally. On a high spec machine you should be fine.
When it comes to hardware though, you can't do a direct comparison between Windows and OSX running the same CPU and the same amount of RAM etc. A very generalised summary would be that given the same CPU and the same RAM OSX will run faster but there are so many other things that can affect things that even this isn't really a fair summary and the amount it runs faster could be a lot or very little depending on these factors.
Will a Mac mini run Aperture? Yes. Will it run it well? Maybe. It will depend on how much RAM you have, whether your library is on the system drive or an external one, how big the library is and whether your library uses referenced files or not. You would definitely be better off buying a 27" iMac. Yes they are expensive but you will not only have a very powerful computer more than capable of running Aperture but you will also have one kick-ass screen that will really show off your photos to their absolute best.
Buy a Mac, don't buy a Mac. The choice is yours. Personally I wouldn't buy a Mac just to use Aperture. Aperture is good but not that good. Buy a Mac because you want or need all that a Mac has to offer.