Is there any reason to have both? Do they offset eachother or complement eachother?

"Your http://fallout.wikia.com/wiki/Melee and http://fallout.wikia.com/wiki/Unarmed attacks do more damage, but less critical hit damage.
More specifically, your Melee and Unarmed damage is increased by 20%, but your Critical Hit damage is reduced by 60%, but only for those two weapon types. Since you inflict more damage consistently with Heavy Handed though, Critical Hits are less of an issue, unless the player relies on http://fallout.wikia.com/wiki/Sneak_attack_critical as a major source of damage or if the character criticals often due to perks, Luck, and high weapon modifier (certain perk/weapon combinations give you a guaranteed chance to critically hit)."

If I am reading this right, if you attack while sneaking you will be ok.

That's exactly what I needed to know, thanks Styles

Not sure what kind of character you're going for, but if I go heavy handed usually I just use luck as a dump stat. I don't think investing stats into offsetting is worth it. 60% less damage is a lot of dam to lose on a crit so I don't bother trying to make up for the loss.

Heavy handed with an explosive build is great. You're not gonna get crits with your explosives anyway, so all the more reason to dump luck and invest your stats somewhere else.

I think the nail board has a 0 crit rate and the rebar club has a .5 crit rate. Those might be good options for a 0 luck / heavy handed build.

What kinda character were you going for anyway?

Pure melee, knives primarily. Never tried it, always used guns so I'm looking for pretty much the best build. Lots of sneak attacks stuff like that

I wouldn't use Heavy Handed and 9 luck together. If my luck was at a 5 and I focused on melee weapons then that's a different story. If I have 9 luck, I'll be wanting those critical hits.