Hi ChaosLord,
The Mini ITX Case proposed is a Mini ITX one and every Mini ITX has an external pico atx power suppy, like the ones for laptops for example.
Internal ATX supply are for ATX / Micro ATX case, so, it takes more place on your desktop.
Each one can be used for FPGA Arcade board until you take the ATX adapter done by Mike for more security (included in the propopsition you have received).
I think it's just a matter of place on your desktop !
Also, the case I have suggested is a VESA compatible one, so it can be fixed behind your monitor like I show it on my photo
HERE.
Thanks, Laurent aka Faranheit