Axe for scrakes which you stun and can take out by hitting the head a few times. Also for kiting fleshpounds without taking any damage.
Good luck doing this in a pub game. "ZOMG FP! UNLOAD ALL ROUNDS INTO IT IMMEDIATELY!" They'll rage it on you and you'll get hurt everytime. Better to let the pubbies rage it, then you hit it in the back of the head for huge damage.
Also, Fire Axe alt-fire can 1-shot Husks and Sirens. Pop around a corner, insta-kill 'em, retreat around corner.