Getting back to the original question...
I got a 2.6 GHz i7 late 2012 MacMini. I got the standard 5400 hard drive and upgraded to 16 GB of ram through macsales. I got a copy of FCPX for editing 1080p home video taken on a Sony videocam (AVCHD format). I should mention also that for my 'scratch drive' (or whatever it's called), I use an external hard drive (7200 rpm plugged into the newertechnology 'Voyager Q') connected via USB 3.
At first, I just attempted to convert 7 minutes of AVCHD to BluRay (got a BluRay burner from macsales as well). This went fairly quickly, about 9 minutes of processing, then about 7 minutes to burn the disk. Being a weekend warrior FCP user, I was happy with this.
A few weeks later, I was watching my 10 year-old daughter put together a thank you card on Print Shop, and was shocked at how fast and nicely she was putting all sorts of graphics, layout, and text modifications, etc. on the page. I thought it would be interesting to see what she would do with FCPX and some home video. I showed her the basics (pretty much all I know anyways), and let her take over. Within about 3-4 minutes, she is making our cat make growling sounds, adding rain to scenes, and filtering other shots through 'bug-eye'. She changes some of the color filtering as well, and put a few transitions in. Well, I hate to admit it, but she did not make friends with my mac mini. Within a few minutes, every core was maxed at nearly 100%. After she had been at her editing for about 10 minutes, I had her stop to see how long it would take the background tasks to catch up. Approximately 40 minutes later, the processors backed off below 90%. I got the feeling that my computer wished it had a video card.
Recently, I took 70 minutes of 1080p AVCHD video and turned it into a DVD using FCPX. This was a very easy process, and it took my computer about 2-hours to crunch the data before it started spitting out DVDs.
I hope this gives you a ballpark idea what to expect using a mac mini with FCPX.
As for me, I can't wait for the new Mac Pro....
on second thought, I've been waiting since 2010 - what's another year...