I've played the whole Beethoven and the 1st mvt. of the Mozart, and I found the Mozart to be on a whole new level. I think it requires much more attention to detail and is just harder than the Beethoven imo.
Comparing the "grades" of these pieces isn't very useful. This doesn't make any sense to me ... you should, in theory, pay as much attention to detail in Beethoven as in Mozart... I would suggest sticking with the Mozart, or picking an earlier Beethoven sonata before starting with the Moonlight sonata. perhaps pick another Mozart Sonata. K 310 and Moonlight are both jumping into the deep end.