For me, BF becomes a camp battle. MK's love to try to dair camp, nado camp, shuttle loop camp, etc by hiding under the other side's platform, and it always works somehow.... It's a fun stage, but I don't do amazingly there in that matchup.
I actually prefer YI as my main neutral against MK. Peach can camp under the platform , has more options to cover all of her zones, and MK is limited in the air. The only things I don't like about it is that MK's short hop aerials can get a little tedious to deal with, and his shuttle loop kills earlier than usual. But besides that, Peach's fair can get a nice kill on MK, turnips are great with the limited aerial mobility, and MK is trapped a lot of the time. I've gotten Anti to last stock last hit several times there (I beat him in friendlies there, but not in ranked matches =/ )
And for some reason, I've played a few MK's who know exactly what they're doing on FD. If they go aggressive, then I get trapped a lot. Even though there is a large space for turnip camping, I do lose to a few select MK's there...
And I've never tested out Green Greens too much yet. Maybe I should try it out...