When this question is asked, people typically only discuss the bacterial community of the rock. Any reasonably mature live rock will have a pretty good bacterial community. Any dry rock (whether artificial, mined, or real coral skeletons) will have effectively none.
What I dont think gets mentioned enough is the porosity of the rock. Almost all of the manmade and mined rock I've seen appears to be completely non-porous, with only a thin layer of cavities on the surface for bacteria to colonize.
I've broken up a lot of dry mined rock, live man-made rock (cultured in Fiji) and dry pukani. The difference in porousity is huge. Literally like the difference between a sponge and a brick. The point of live rock is to provide surface area for bacterial colonies. For these colonies to filter the water, they have to be in contact with the water. Coral skeletons have a network of cavities throughout. Manmade and mined rock are solid bricks. Based on these observations, I would bet money that 1 cubic inch of dead coral skeleton houses more bacteria than a cubic foot of dry rock.
This is not to say that I think artificial/mined rock hurts a tank somehow. I just think its absurdly ineffective relative to coral skeletons.
These days, if I'm gonna bother taking up space in the tank or sump with it, it had better be 100% dead coral skeleton. I don't care much if its "live", wet, or dry... but I'm done wasting space in my tank with what are effectively non-porous bricks.