Heavy handed is pretty good if you are not focused on crit only builds. Pretty much everything has been said like take melee first and then get unarmed up for the perks. Ranger takedown is the best as well as getting paralyzing palm. Get slayer, use rushing water and turbo and watch everyone get sliced (or punched) like they were butter!
Heavy Handed is only decent towards several heavy duty weapons. After that, no, Heavy Handed svcks overall on that part. Without that Trait, your critical damage boost would rocket up to 3.375. Do you know how powerful that is? here's an example:
With Chance's Knife, you merely get 22 Critical damage with 22, making it 44. Not much for now, but with Better Criticals, Just Lucky I'm Alive, along with Elijah's Ramblings, it boosts the critical damage to:
22x3.375=74.25 critical damage +22=96.25 damage per swipe. that's extremely powerful right off the bat.
now with Heavy Handed: 22x0.4x1.5x1.5x1.5=29.7 critical damage+26.4 damage=56.1 per swipe
you basically nearly wipe out almost 50% of your potential power, this is only useful for weapons that have a low chance or small weak Critical damage, you might as well get the damage boost. (the lowest I noticed so far in critical chance is x1 in Melee and Unarmed, and the highest you can get on that without magazines is 33%, which is actually pretty decent considering how merciful the game is with criticals. With Comprehension and True Police Stories, that boosts up to 43%, which is pretty deadly on it's own right there.)
Even then, Heavy Handed drops very rapidly in usefulness, even something as the Chainsaw, with 8 Critical Damage. Sure it looks pathetic, but with all the critical perks, it shoots up to 27 critical damage, and automatic Melee/Unarmed weapons check for criticals 30 times per second I believe. So the damage basically shoots upwards once you start rolling in crits. Like I said, Heavy Handed is overall a very terrible trait. My opinion? Go for Built to Destroy.