You get +4 points of melee damage, but your critical hits have a -30% modifier to the critical hit tables.
Fallout: New Vegas
Your melee and 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 Sneak attack criticals 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).
Mathematically, Heavy Handed will provide a net benefit if
where each component is considered after all modifiers except Heavy Handed.
For example, a character with 5 luck armed with a machete has a 7.5% critical chance and does 11 critical damage, equal to the base damage. This satisfies the above condition, and expecting a critical hit approximately every 13 swings, a machete's damage with and without Heavy Handed should work out to this:
Without Heavy Handed: 13 swings * 11 damage + 1 crit (+11 damage) = 154 damage
With Heavy Handed: 13 swings * 13.2 damage + 1 crit (+4.5 damage) = 176.1 damage
By contrast, a character with 10 luck armed with Figaro has a 40% chance to critical and significantly higher critical damage than base damage, not meeting the criterion. Over 10 swings, the average damage works out to:
Without Heavy Handed: 10 swings * 8 damage + 4 crits * 16 damage = 144 damage
With Heavy Handed: 10 swings * 9.6 damage + 4 crits * 6.4 damage = 121.6 damage
Synergizes well with the Loose Cannon trait and/or Heave Ho! perk due to the usefulness of throwing spears with this trait. It can be somewhat useful with Better Criticals due to weapons such as the throwing spear and cattle prod, which inflict greater damage on a critical hit or sneak attack critical with both Heavy Handed and Better Criticals.
Example: a Crit DMG of 10 would be reduced to 10 * (1.0 - 0.6) = 4. With Better Criticals it becomes 4 * 1.5 = 6. Elijah's Ramblings then increases the damage to 6 * 1.5 = 9.
You swing harder, not better. Your attacks are brutal, but lack finesse. You rarely cause a good critical hit, but you always do more melee damage. You do +2 points of damage in melee combat (hand-to-hand or non-ranged weapons). Your critical hits have a -30 modifier to critical chance. This trait cannot be selected with Finesse.