With high brawling skill, luck, strength, and agility, plus some super-heavy armor such as Pseudo-chitin armor or Power armor, the character will be able to go toe-to-toe with Base Cochise robots, the Scorpitron, or even the Night Terror in Finster's Head.
Armed with one, your character will grin and scythe down pretty much anything in his path. The Proton Ax is definitely the most powerful melee weapon in the game.