Who would win in a fight between Hellboy and Superman?

It is debatable. Both can deflect bullets, both can self-heal, and both have relative super-strength. Superman would have an advantage in being able to fly. He also is less easily injured, unless he is exposed to kryptonite. Hellboy, on the other hand, does not have a weakness to kryptonite so this would not affect him. Hellboy could also grab boulders and trees to throw at Superman. Hellboy can be more seriously injured despite his superstrength and near invincibility. Because of this, it may be superman that would win the fight as long as Hellboy does not have kryptonite.

It should be noted, however, that Hellboy has the power to summon demons and can control the dead, so he could probably raising up a demonic or undead army to fight Superman whereas Superman would just be by himself, so maybe it would be Hellboy after all who would win the fight.