I play Raph
First off, @Vex uses power blades and therefore is the inferior beetle.I also think it's in Crow's favor until Beetle gets a knockdown. His zoning is pretty easy to navigate with Crow, but that's not really the way the MU should be played. I mean at all lol. If you're playing purely to keep Crow out, you're not going to get very far.
I play Vex on the regular and the scariest thing to me is when he pops trait and starts playing footsies. Jumping is generally a bad idea because of Beetle's antiair properties on his F2. F1 is out of the question because it can be very easily whiff punished with his 6f D2. That means you're playing for scoring a F2-gas blast and chasing down to make reads on Oki.
Meanwhile, if Beetle can score a knockdown with F2, he can freely flight pressure Crow into mixes and there really isn't much that Crow can do about it. Unless I have a read, I generally pushblock. I haven't explored wakeup teleport, but it seems like a bad option *especially* in the corner when Beetle can meaty a J3 into flight pressure.
The average Crow player will still probably beat the average Beetle player. But if you want to learn how to play the MU well, take tips from Vex and pop that trait my guy.
But in all seriousness, there is a good chance that I'm overreacting. If the Beetle is on their top game with power blades we can play the footsie game with scarecrow. It's just unfavorable for the most-part, because it's easier for scarecrow to get his game going than it is for us. Like you said, we rely on a knockdown. Which is not as easy for us as it is for scarecrow in this matchup.
I don't think this matchup is a hard 6-4, it could be 5-5 but slightly leaning towards Scarecrow just because of how much easier it is for him to 'get going'.