Like many battle manga, both have grand, spectacular battles between super-powered fighters.
What links them closer is that both have characters who are the strongest among their kind. They have since grown bored with their powers and wish to face an opponent that can make them feel the thrill of battle again. In One Punch-Man, this relates to the main character, while in Valkyrie's case, this may only apply to the two characters in the first battle.
Vastly different series with incredibly similar setups.
Both involve the gods wishing for humanity to end due to the latter's cruel nature. In Valkyire's case, this is voted for by a council of gods, while in Priapus, Zeus decrees this alone. Zeus appears to be the main ruler in both stories.
From there the two manga go in different directions:
- Valkyrie is a battle manga where humanity fights against the gods to decide mankind's fate
- Priapus is a yaoi manga where the titular character aims to turn every man gay to peacefully end mankind
Nevertheless, both feature muscular men bashing each other.