I feel MM vs Falcon is in MMs favor by a bit, neutral cant be lost and we have a very strong ledge game vs him.
only slightly negative MUs for MM for me is fox, Mew2, Shiek all the other we have significant neutral advantage but still feel its around even just because how we kill and damage output from some chars.
Having a fantastic neutral is all well and good, but it doesn't mean much if you can't get the kill and last time I checked, you have to do it twice to win a game, at least 4 times to win a set of 3, and at least 6 times to win a set of 5 which is around top 16 or higher at a noteworthy tournament. Some tournaments even do 3 stocks. Luckily for us we can, though we do have a more difficult time taking the stock compared to most of the really good characters.
Me personally, I feel like Fox and Shiek don't just barely win against Mega Man. They both have a clean +1 advantage over him. I can definitely see why Mewtwo may be perceived as a slighty negative mu. If you take Samus and give her a much faster run speed, a grab that doesn't suck, a reflector, a really good fair, and two scary kill throws (b-throw and u-throw), you get Mewtwo with the only downside is that he is a lot lighter than Samus.
I will say though that if Shiek didn't have a projectile that shuts him down, this mu would probably be a lot closer than it currently is.
Now, onto Captain Falcon!
This is just me speaking, but I find
to have some similarities to
as they both are really fast characters and are combo heavy characters that want to apply as much pressure on you as they possibly can as well as giving Mega Man a bad time. While Captain Falcon is a lot heavier than Fox is, Fox has a lot more attributes to make a mu for Mega Man harder than Captain Falcon has.
For one, Fox has a reflector while Captain Falcon doesn't. Due to this, he has a more frustrating time having to deal with the projectile onslaught that the blue bomber can dish out at him. Another important difference between the two is that Fox has a better pressure and neutral game against Mega Man than Captain Falcon does. Outside of Captain Falcon's fantastic grab game, hardly any of his moves are safe on shield so he kind of has to heavily rely on getting the grab or playing mind grabs as he is one of the few characters in this game who can dash dance like you can in Melee albeit a lot harder to do, but it's still a thing so do keep that in mind. Fox also has more kill setups on and offstage like jab>u-smash or can get 3 hits off of fair>fast fall>footstool=gimp. Captain Falcon doesn't really have that many kill setups against the blue bomber, but d-throw>knee can be a thing depending on di and if you air dodge or not.
Good Captain Falcon players like Fatality will try to keep an eye out if you air dodge and if they guess correctly, you'll be tasting the knee of justice. As others have stated, while extremely underutilized, ducking is important in this mu and is an option that we should use in general as he has a really low crotch.
Trying to get back onto the stage and reset the neutral can be an absolute nightmare at times. It's worth noting that his u-tilt has a spike hitbox and at high percents near the ledge, getting hit by Captain Falcon's d-tilt can launch you pretty far downwards which can potentially end up getting you gimped. His jab limits your ledge options since it covers regular getup, getup attack, and his jump somewhat. Therefore, you're only left with rolling which will probably end up getting you back offstage as he'll be expecting it and can make it happen thanks to his speed.
I find this mu to be in
's favor 55:45 over
as his damage output and combo game is a few leagues above Mega Man's is despite having a stronger neutral than Captain Falcon. But, I do think though that as more and more time goes by, this mu will probably end up being even if we can do a better job keeping Captain Falcon out and can capitalize on getting the kill/gimp whenever he is offstage.