Hellboy outfootsies a lot of characters with a safe hit-confirmable mid into high damage and leads into pressure. You can't zone him because of gunshot and leap so you have to fight him up close which is where he also excels at. Everytime Hellboy touches you and leaps you're in the blender, having to guess between overhead/low/cross-up/non cross-up/cancel. Anti-airing him isn't as easy as people say and is super risky because he can dash cancel out of leap at any point or cancel into a mid leap and whiff punish your d2. Then he's also got an armored trait that keeps him safe and allows him to do whatever he wants. Probably has the best anti-air in the game, one of the best B3s, a great wake-up attack, launching command grab, meter build, etc.
IMO Hellboy doesn't seem to have any weakness and seems to do everything very well. He can be just as silly as Supergirl and Catwoman, maybe even sillier.
I feel like Batman has always been underrated. No one was talking about how good he was before E-League and his nerfs didn't really affect him that much. He's still got a plus on block 50/50 vortex that leads into high damage or another 50/50. His 223 is a safe hit-confirmable meterless launcher into B3 which breaks the rule of having to spend a resource to launch, but in Batman's case he's spending his resource on MB Grapple to vortex you.
Batman's trait literally does everything in the game, and all you need is 1 bat. It's a neutral killer, it anti-airs, it punishes forward dash, allows you to convert off everything into a vortex, gives you safe launching 50/50s, lets you safely stop walk back and combo with Slide, sets up his j2 50/50, allows you to get in for free, gives you a safe MB Roll out of the corner, punishes moves that are -2 on block, blows up gaps, stops your opponent from pressuring you, makes it always his turn during pressure and he can release bat at any time and go into +7 or more on block. With 2 or more bats, he armor breaks and has a real 50/50 with F3 or F3 cancel MB Roll.
I'm not sure who Batman loses to, but he probably destroys a lot of characters who don't have an answer for trait. I think his strengths far outweigh his weaknesses, if he has any.