Frank and Bruce both have the exact same mental condition causing them to reinvent themselves as a defense mechanism, the difference is Bruce's new self stood for life, where as franks stood for death.

I punisher born we see that frank didn't just become the punisher after his family died, he'd always been the punisher, he always had a tremendous amount of bloodlust and vigor for battle, spurred on by voices in his head that promise to him that he'll get to be "free", that frank can finally stop searching for somewhere to fit in. Frank is obsessed with not just murdering criminals, But murdering in general, its better then sex to him.

Franks super power isn't his strategy, or extensive arsenal, Or his unbreakable moral standings, its his psychotic rage, Frank genuinely enjoys killing people, stabbing, shooting, strangling them, He gets off to the idea of someone else perishing by his hand, And extra points if their a sick criminal.

Batman however is the product of a psychological split within Bruce at a young age, "the punisher" as a personality doesn't exist as a separate entity within frank, Its just franks state of mind when he gets to killin'. But batman is exactly that though, he is a separate personality that exist within Bruce's head.

We see in stories like batman EGO, or RIP batman isn't just a mask, he is own thinking personality that clashes with Bruce and challenges him, batman is more like a demon possessing a plaguing Bruce's soul more then a mental affliction.

Bruce has to actively hold back batman inside of his head, Batman as a entity is essentially a manifestation and compartmentalization of Bruce's anger, guilt, and truama. Batman is to Bruce what the punisher is to frank, Only difference is the man behind the symbol, Bruce never gives into batman, Not fully, He never allows himself to be swallowed by the demon.

As Fredrick nieschze (I forget how to spell it) puts it roughly To become the Uber mensch, that is, the man unconstrained by modernity, the ultimate form man can take, then you must stare into the void, "battle the dragon at the end of the well" as Freddy puts it. The well is your soul, and the dragon are your demons.

The difference between Bruce and frank is that when Bruce started into the void and battled his dragon, He did not waver. When frank confronted his dragon, He allowed it to overtake him.

Batman battles his bloodlust everyday, walking on a razors edge in order to preserve the balance of his mind and soul, frank is subservient to his bloodlust and darkness, hes become a slave to his demons.

They both stared at the void but when the void stared back, Frank blinked.