Missions to Mars are mostly planned with in-orbit refueling, so launching from the Moon would not be easier. The Moon in general is also a rather harsh mistress. You have 2 week long nights with absolutely brutal extremes of heat and cold ranging from -133C at night to 121C during the day, no atmosphere whatsoever, a fraction of the gravity of Mars, regular bombardment with meteorites and so on.

A Moon base will be a far harsher place than a Mars base. Mars is bizarrely similar to Earth - nearly the same length of day/night, similar axial tilt so similar seasonal patterns, nearly the exact same land area, and even calm weather. Notably the 'raging dust storm' in "The Martian" that was used to set up the crisis for the movie was one of the few things that was intentionally faked. The low atmospheric pressure on Mars means even the most brutal dust storm would feel like a slight breeze at most. It's also telling when you need to fake something to create a crisis, in an otherwise very hard sci-fi book!