This is especially interesting considering that the Service Module and LM RCS used the same thruster hardware (Marquardt R-4D). The R-4D was originally designed for MMH and first flew on Lunar Orbiter 1:
Marquardt experimented with a variety of liquid storable propellants. They selected NTO and MMH for their thrusters. However, government requirements led Marquardt to also use Aerozine 50... In the last couple of decades, Marquardt learned how to use the same thruster with several different propellants, namely, hydrazine, UDMH, MMH, or a mixture of any of these.
Both fuels deliver nearly identical specific impulse; Aerozine-50 is a couple of percent denser than MMH, so would produce very slightly more thrust for the same volume flow rate, but that kind of marginal performance difference wouldn't have been a consideration for the RCS thrusters.
MMH has a much lower freezing point (-52ºC) than Aerozine-50 (-7ºC). (Aerozine was developed for the Titan II, an ICBM usually sited in heated silos, thus its density impulse advantage was more important than its thermal range.)
The LM could pump fuel back and forth between the ascent engine and RCS tanks, which offered some contingency options, but there would be very few situations where it would be necessary or useful.
If I had to guess, I'd say the freezing point made MMH generally preferable, but that the LM designers preferred a single type of fuel -- remember that the CSM and LM were developed by different contractors (North American and Grumman respectively) with different engineering priorities. I didn't find any insight into the fuel selection in Kelly's book on the LM.