A couple of interesting hypotheses are given for the difference in Why Do We Have a Two-Faced Moon?
Both hypotheses stem from a small planet colliding with Earth - The Giant Impact Hypothesis followed by a period of heavy bombardment by big asteroids.
The first states,
... the impact which formed the Moon actually formed two moons. One was big, and forms the bulk of the Moon as we know it today. But a smaller moon also coalesced out of the ejected material, and was on a very similar orbit to the bigger moon. After some time, the two collided.
But this wasn’t a high-speed impact. Some orbits allow for a low-speed collision, which would be a lot less explosive. If that were the case, the smaller moon would splash, essentially, touching down on the Moon’s far side and flowing like liquid over it. This would create a lopsided Moon, with a thicker crust on one side than the other, as we see things now.
The second hypothesis states,
After the Moon-forming impact, the Earth and Moon were very close together, and both were very, very hot from the impact.
After it first coalesced, the Moon may have only been 20,000 kilometers away, and would’ve loomed huge in our sky.
And it would’ve been hot. The surface would have been molten from the energy of impact, and that means the Earth would’ve been around 2,500° C (4,500° F). It would’ve stayed hot for some time, too.
During that time, the Earth and Moon would’ve been heavily affected by their tides on each other. Tides are complicated (read all about them here), but one effect they have is to slow the Moon’s rotation until it spun once for every time it orbited the Earth, just as it does now. That means very quickly after it formed—incredibly, in just a few months—one side of the Moon would always face the Earth, and one side would face away.
The side facing the Earth would have that huge, glowing hot blast furnace radiating away down on it.
... refractory chemicals (ones that retain their strength when heated) would have gotten mixed in all over the Moon’s surface, but would have preferentially condensed on the far side of the Moon, where it was colder due to the lack of heating from the Earth. These would have formed feldspars (in this case, minerals that contain aluminum and calcium) that would have caused the newly formed crust to be thicker on the far side.
The far side of the moon cooled down, while the near side remained hot.
The temperature difference played an important role in the formation of the moon's crust.
The crust has high concentrations of aluminum and calcium, which are hard to vaporize. Calcium and aluminum would have been the first elements to "snow out" as the vaporized rock cooled, and they would have remained in the atmosphere on the moon's far side. Eventually, those elements combined with silicates in the moon's mantle to form plagioclase feldspars. The far side's crust had more of these minerals, and thus became thicker.
The seas themselves were formed after huge meteors crashed into the moon's Earth-facing side, rupturing the crust and letting the basaltic lava beneath burst forth. The crust on the far side was too thick for the meteors to penetrate, in most cases, leaving the rugged surface we see today.