Nothing to do with the CPU. BIOS has the activated key integrated, in my case 'Home', and likely, yours also. The install process is reading this info from BIOS, and because the image only has the 'Pro' version at hand, it defaults to the 'base' install, which is Enterprise, as nuhi pointed out above. If 10 Core was available from the image, then you would find it installs the 'Home' version, and activates perfectly fine, as this is what these laptops came with in first place.
The solution is simple, as posted above. Enter default install key in 'Unattended' for the version you wish installed, and it should then install correct version, in my case Pro. Then, providing you have already activated your chosen version before on that hardware, it should then re-activate as normal.
If your not running the image through NTLite, then I suspect an ei.cfg and/or PID.txt would allow you to do the same.