Likewise it also is more performance in games than a Core i5 4570R too.
Go on some other enthusiast forums which people do ITX builds on(Overclockers UK and Overclock.net being two examples),and maybe you should look at some of the low profile mini SFF builds on them.
The base Core i5 4570R based Brix in the UK is at least £400 excluding HDD,RAM and OS. That means with Windows,8GB of RAM and a HDD,at least £550. Plus the Brix has been documented to have throttling issues at least for the Core i7 4770R version:
http://techreport.com/review/26166/gigabyte-brix-pro-reviewed/4
The Core i5 4570R,has only 4MB L3 cache,which is less than desktop Core i5 CPUs(same as high end Core i3 models),and has a significantly reduced base clockspeeds too:
http://ark.intel.com/products/76640/Intel-Core-i5-4570R-Processor-4M-Cache-up-to-3_20-GHz
So instead of 3.2 to 3.9GHZ with 8MB L3 cache,you have 2.7GHZ to 3.2GHZ with 4MB L3 cache.
The Core i7 4770R runs at upto 1.3GHZ for the IGP and the Core i5 4570R runs at upto 1.15GHZ instead.
So the SKU is going to have lower performance overall than the Core i7 4770R.
Considering you can get very small SFF low profile mini-ITX cases from companies like Wesena,Antec(ISK low profile series),etc and having seen the builds people and mates have done in them,the R series Brix appears to be a solution looking for a problem at its current price. If Intel had a cheaper Core i3 version with the same IGP section it would make more sense.
Its even worse now you have a new Brix model with a downclocked HD7770. It comes in both AMD APU and Intel ULV CPU form,and most likely to be better for running any games too,especially with the Intel version.