I don't play Falcon much, prefer Ganon myself. So these might not be too accurate.
His punishes more or less depend on his opponents making a mistake or the wrong decision, there's not a lot Falcon is in control of.
That's the idea of a bait and punish character.
Typically, bait and punish characters doesn't have a solid game plan, they rely on their opponents' mistakes to win.
Falcon is an aggressive bait and punish where Bayonetta is a more patient bait and punish character.
Falcon can easily punished Bayonetta's dodges due to his speed and grab. Most of Bayonetta's options are unsafe against Falcon.
His edge-guarding is good, but I have no idea how you expect anyone without a disjoint or counter to edgeguard Bayo, let alone Falcon.
It is hard to edgeguard her no doubt, but it is completely possible to do so.
Witch Twist has surprisingly low horizontal range and ABK has a small window to punish.
I saw a Utilt spike before.
Edgeguarding Bayonetta is still kinda hard, so practice it and mix it up.
His neutral is above average, but I wouldn't call it outstanding. All he's really got is bair and uair, sometimes nair, and tomahawks.
He got great speed and a great grab range. Both of which Bayonetta lacks.
His neutral against Bayonetta is definitely great.
He has like no range so he's always running the risk of getting hit by something like Witch Twist OoS.
Range didn't hold Mario back, like Mario, he possess a fast grab and good options against shields.
And as far as KO options go, like his punish game, they rely on the opponent making a mistake or Falcon getting a read.
Remember Bayonetta's special landing lag? That is a great moments to execute his KO, just don't be predictable.
As hard as it is to land his KO moves, they also hit extremely hard too.
If you play safe against Falcon there isn't much he can do to take your stock.
It is significantly harder to play safe against a Falcon compared to Bayonetta. Bayonetta tends to have multiple unsafe moves and has the special lags.
Playing safe is always a bait and punish character's biggest weakness. But that's is the MU for ya.
And his kill throw doesn't really do anything until like 150%.
So does Bayonetta's, I think Bayonetta's kill throw is weaker.
I think with equal experience against each other, the MU is pretty even.