“The critical hits you cause in combat are more devastating. You gain a 20% bonus on the critical hit table, almost ensuring that more damage will be done. This does not affect the chance to cause a critical hit.”— in-game description, Fallout
With this perk, a +20 bonus is applied to the Critical Hit table roll, which effectively moves it up one table entry, ensuring a more damaging type of hit.
The perk does not affect the chance to cause a critical hit, just the damage.
Taking this perk is the only way to get a critical hit roll over 100, which yields instant death in half of the hit areas.
The instant kill effect is independent of damage. It's even possible to kill something without any damage.
Synergises well with Sniper and high Luck, as these convert each shot to critical.
Scripts triggered by a critter's death do not fire upon "instant-death zero-damage criticals" (Pariah dog is one example). These can be prevented by also having the Living Anatomy perk which makes zero-damage attacks impossible. Allegedly, Bonus HtH Damage and Bonus Ranged Damage perks do the same.
Fallout 3 and Fallout: New Vegas
“With the Better Criticals perk, you gain a 50% damage bonus every time a critical hit is scored on an opponent.”— In-game description
With this perk, the weapon's critical damage is increased by 50%.
Use weapons with a high critical multiplier and high critical bonus damage to maximize damage per second.
Due to the way in which the critical hits are determined, any weapon that produces multiple independent projectiles per shot (e.g. the combat shotgun, various unique scattershot laser weapons) will individually check each hit for a critical when firing outside of V.A.T.S. and do the full bonus critical damage for each success. Since criticals are automatic in sneak mode, point blank sneak attacks with one of these weapons will inflict X times the critical damage rating of the weapon, where X is the number of individual projectiles fired; for some weapons this outstrips the damage of the Fat Man.
In Fallout 3, having only 5 Luck and not the required 6 in order to obtain the perk, a character can equip the Lucky 8-ball which yields +1 to Luck. It is then possible to get the perk on the next level up, and the perk stays even if the 8-ball is removed.