Ok so It has been awhile since I have posted much and since I have consistently played because I am busy irl.
From what I have been playing the mu feels even to me.
Now first of all Hellboy doe's have a low his b1 however it does not lead to a combo. Most of the time Hellboy's will use the full b1 string for a safe string on block I think its like -2-3 or something can't remember. Other options are to do b12 into leap for the cross up setups etc. He can also do b1 bounce cancel into f3 for the low overhead mix but this is extremely react-able.
Now with leap I do believe it can be reacted to at full and mid screen but up close I feel that's where it gets tricky because up close he will be cancelling into leap or into the + charge or maybe staggering a string etc. Now from my xp playing Hellboy and against him most people will react to the initial dash in the leap that helps them ant air Hellboy especially when they see it cancelled off a string. Now Hellboy's normally bait this by doing a mid range leap over the opponent into a raw Fist of doom cancel instead of the air dash cancel to bait out a button press and whiff punish the opponent trying to anti air. So from my xp when it comes to close range with leap cancels its all about reading what you think your opponent is going to do and that's for both of the players.
But leap can be reacted to full screen for sure. Its also worth mentioning that Hellboy can make a read against a projectile full screen for a punish.
As for Hellboy's wake up it can actually be stuffed pretty consistent with many string/specials even against players that have no experience I have been d1'ed out of my wakeup many many times and against a experienced player I have even been full combo-ed.
The zoning game feels pretty even to me as well if bats gets his trait out then of course he has an advantage to get in or zone some more etc but this is also a good opportunity for Hellboy to trait up with armour to counter this causing a stale mate.
So this is kind of my synopsis I think that the mu is even they both hit hard and have nice setups for the other to deal with their zoning feels even and both their wakeups have flaws being either horrible frames or it can be stuffed.
I hope that this shed's some light and that I touched on each option (Kinda wrote this up really quick) as I said have not played nearly as much as I did in the past I do plan on coming back to the game though.
One thing I will say is if you really want a detailed opinion I would ask
@SylverRye as he is a Batman and Hellboy player who is in the competitive scene and has a crap ton experience than a filthy casual like me.