If the Moon was created by a glancing collision between the Earth and a Mar-sized protoplanet, which seems to be the going theory nowadays, then the Moon was created in Low Earth Orbit during the very heavy bombardment phase of the LHB. Once the Moon became tidally locked -- which would have happened pretty quickly at such proximity -- Nearside was shielded from most further bombardment by the Earth. So Nearside is kind of a fossile from the heaviest epoch of the LHB, while Farside continued to get pelted as the big stuff was swept up, and finally got the fine dusting of the last scraps evening it out. It would also have continued to accumulate crud, which Nearside wouldn't, thus the thicker Farside crust.