I have 2 systems where i can play AOTS and i've noticed this :
The slowest one, has a 560TI card with only 1gig of DRAM, and can run DX11 version with no problem, while as far as i could read, 2gigs of DRAM is the minimum required.
On this system, DX12 version won't start.
I have to install Win 10 for the second system which has GTX770 with 4 gigs of DRAM and check if DX12 version works.
That was just too mention that even on a system without minimum requirements, DX11 version will run, which may not imply DX12 version will.