It certainly makes a difference - entering on the prograde direction relative to the moon's orbit is much more beneficial in outward Hohmann transfer.
The upper image shows the needed trajectory in the planet's frame of reference. The bottom one is from the Sun's reference frame.
Relative to the Sun, given moon moves in an epicycle trajectory. Epicycles have a part that is much faster than "standard" orbital speed around the Sun, when the moon and the planet move in accord, and drops of speed - going into negatives sometimes - when the planet and the Moon go in opposite directions.
Since your spacecraft is at apogeum of its elliptical orbit, its speed is much slower than that of bodies in circular orbit at the same altitude. That means matching speed with a body that moves below speed of circular orbit is easier than with one that is even faster than the planet.
The whole situation, obviously, is reversed if you arrive from outer planets towards inner ones. That is, you still want to meet the moon in its prograde orbit direction, but you meet it on the side where it moves fast relative to the Sun.
Now, there's still the matter of whether to enter prograde relative to the moon's spin. This really doesn't matter unless you plan to land (or deploy a lander) in which case prograde is beneficial, meaning the moon's rotary speed may be substracted from delta-V needed to land, instead of added.