Both are fine. One is more "wordy" than the other without adding any additional information, so good style recommends you use the shorter version.
However, the overall sentence is more repetitive than it needs to be:
The Moon is different from the Earth in that there is no dawn or twilight on the Moon.
I know that there are many differences between the Earth and the Moon, so the use of "in that" is a little awkward since it implies that you are going to present a (somewhat) complete list of these differences. For example:
John is different from Jane in that he is taller, has dark hair, and also is not female.
Since you list only one difference, it makes me question why you didn't include the other differences. If you just intended to describe one difference, it would be more natural to say:
One way the Moon is different from the Earth is that ...