According to NASA [0], you are correct. Furthermore:

"It is likely that each side of the Moon has received equal numbers of impacts, but the resurfacing by lava results in fewer craters visible on the near side than the far side, even though the both sides have received the same number of impacts."

[0] https://lunarscience.nasa.gov/?question=3318

The earth looks huge from the moon. The moon’s diameter is 2,158.8 mi where earth’s is 7,917.5 mi, meaning it looks 3.5x as wide and covers 13.5x the area. So more your fist at arms length than your thumb.

In terms of impact gravity and atmosphere extend that somewhat. Though, that’s still not enough to make a meaningful difference.