As the good Commissar says, the Mk VIIa recon lasgun will be the best at punching through unyielding, infested and carapace armour. It will also stagger those armour types more. The Mk II is similar, but a bit worse owing to the higher fire rate. Then the Mk VId has the “worst” (of the three) armour penetration capabilities, but a lot higher fire rate. But as mentioned above the high fire rate can make it outclass the Mk II in pure damage.
The lower armour penetration capabilities does mean that it will benefit more from brittleness applied to enemies and rending applied to the weapon than the other two marks. Leading to potentially even more outclassing.
I did look a bit closer into the actual tweak values at near/far range, and it looks like there is some discrepancies between the Mk II and Mk VId there. Again I won’t promise anything, but the designers knows about it at least.