Is dual-wielding superior to great weapons for a raging Barbarian?

This question is somewhat two-fold. I am in the process of creating a high-level Barbarian and am trying to determine if it makes more sense to take use dual weapons and capitalize on the additional damage that rage deals versus using great weapons, which benefit more from crits.

The Barbarian’s primal path is Zealot, so he has a revolving door with death. For the purposes of race, we are taking advantage of the revolving door and using the Reincarnate spell liberally. From our Session 0, the character has died and been reincarnated 3 times and is currently a human. I’ve encouraged the DM to kill this character whenever he wants and we’ll reincarnate him as something else. To simplify the complexities of changing race constantly, we are using the following house rules for reincarnation:

  • Retain your original race’s stat bonuses, you lose all the other features.
  • Gain the features of your new race, but none of the stat bonuses.

Currently, the character is a human, but his original incarnation was half-elf. Due to the everchanging nature of his race, assume for the purposes of assessing this, that racial features that improve damage, like Savage Attacks, aren’t applicable since the character could get Worfed at anytime.

The following assumptions should be considered:

  • The character does NOT have the the Dual Wielder feat.
  • The character does NOT have the Great Weapon Master feat.
  • If dual wielding, the character would use a weapon that dealt 1d6 in the main hand and 1d6 in the off-hand (I don’t believe there are any light weapons capable of dealing more than 1d6 damage).
  • Character has 18 Strength.
  • For the purposes of damage calculation, assume the character is raging.
  • No multi-classing.
  • Almost always fighting recklessly for Advantage.
  • Assume the character’s race is not one that provides a bonus to damage or critical damage (like half-orcs)
  • Do not account for plusses due to magic weapons.
  • ASIs are used in a manner that doesn’t increase damage. For example, on boosting Con or Dex. Or on feats that don’t increase damage.
  • Strength adjustments at level 20 should be considered since it is a class feature.

With those assumptions in mind, can someone advise me on which fighting style, on average, deals more damage per round considering the damage bonuses from the Barbarian class features? If the damage optimization changes, at what levels does that occur?