Two-weapon fighting or Two-handed fighting, which is better?

Two-weapon fighting or Two-handed weapons? It can be a tough question for some, and both can be a fun aesthetic to character building. From a numbers perspective though, which deals more damage? Well this is actually a somewhat complicated question, and it depends on if you mean in a single hit, or over the course of a combat encounter.

As you will see, there are benefits to both options. In summary, two-handed weapons are great for burst damage on a single target, which benefit more from bonuses to attack rolls, and two-weapon fighting deals more consistent damage in smaller attacks (attacking single or multiple targets) which benefit more from bonuses to damage rolls.

How these calculations are done are through average damage per turn. For a d6 it is 3.5, (normally rounded to 4) as is per the usual with dungeons and dragons in 5th edition as can be seen in stat blocks throughout the players handbook or monster manual (health increases per level in the players handbook for example). Also it assumes that there is a 50% chance to hit the enemy, meaning the average damage will change when attack a creature that has a higher/lower AC or adding buffs. It also addresses classes that gain extra attack

Two Handed Weapons

Archery
Archery Fighting Style - Increase attack rolls by +2
Sharpshooter Feat - Decrease attack roll by -5, increase damage roll by 10
Longbow - 1d8 piercing damage
Extra Attack
Viable Classes - Fighter and Ranger
                                 Hit Bonus
Modifier                  +0%              +5%          +10%             +15%          +20 %           +25%

0	10.15	11.6	13.05	14.5	15.95	17.4
1	10.85	12.4	13.95	15.5	17.05	18.6
2	11.55	13.2	14.85	16.5	18.15	19.8
3	12.25	14	15.75	17.5	19.25	21
4	12.95	14.8	16.65	18.5	20.35	22.2
5	13.65	15.6	17.55	19.5	21.45	23.4

Great Weapon Master
Great Weapon Fighting Style and Great Weapon Master Feat
Great Weapon Fighting - reroll damage on 1 or 2
Great Weapon Master - penalty of -5 on attack and +10 on damage
Greatsword or Maul - 2d6 damage
Viable Classes - Fighter and Paladin

                          Hit Bonus

Modifier	+0%	+5%	+10%	+15%	+20%	+25%
0	9.2623	11.11476	12.96722	14.81968	16.67214	18.5246
1	9.7623	11.71476	13.66722	15.61968	17.57214	19.5246
2	10.2623	12.31476	14.36722	16.41968	18.47214	20.5246
3	10.7623	12.91476	15.06722	17.21968	19.37214	21.5246
4	11.2623	13.51476	15.76722	18.01968	20.27214	22.5246
5	11.7623	14.11476	16.46722	18.81968	21.17214	23.5246

Great Weapon Savage Attacker
Great Weapon Fighting Style and Savage Attacker Feat
Great Weapon Fighting - reroll damage on 1 or 2
Savage Attacker Feat - Roll damage twice and take the highest
Greatsword or Maul - 2d6 damage
Viable Classes - Fighter and Paladin

                            Hit Bonus

Modifier	+0%	+5%	+10%	+15%	+20%	+25%
0	10.65575	15.23772	16.62297	18.00822	19.39347	20.77871
1	11.65575	12.82133	13.9869	15.15248	16.31805	17.48363
2	12.65575	13.92133	15.1869	16.45248	17.71805	18.98363
3	13.65575	15.02133	16.3869	17.75248	19.11805	20.48363
4	14.65575	16.12133	17.5869	19.05248	20.51805	21.98363
5	15.65575	17.22133	18.7869	20.35248	21.91805	23.48363

Strengths

Archery - Archery provides great burst damage that benefits greatly from attack bonuses. Additionally this is done at a significant range, reducing the need for high defenses

Great Weapon Master - Like Archery, Great Weapon Master provides excellent burst damage, and benefiting a lot from attack bonuses. It also has the potential to deal even more damage as a bonus action, when reducing your opponents to 0 hp.

Great Weapon Savagery - Great Weapon Savagery gains benefits from both attack and damage bonuses in a more balanced way. It has the potential to deal more damage on average without outside help.

Weaknesses

Archery - Like all ranged attacks, environmental and positioning factors can have a big impact on your ability to be effective in combat.
Great Weapon Master - You have a lower chance to hit, so some turns may feel uneventful since you will miss more often.
Great Weapon Savagery - No extra or situational benefits. Additionally you will be rolling and re-rolling quite a lot of dice, so its good to be organized.

Powerful options

Archery - As a Ranger, take the horde breaker option for the potential to do immense damage in one turn to two opponents. As a fighter the Battle Master archetype allows you to increase your ability to maneuver yourself and allies with , as well as negate the disadvantage penalty from adjacent enemies with the Feinting Attack maneuver
Great Weapon Master - As a fighter, take the battlemaster archetype and the Precision Attack maneuver to increase the odds of landing that heavy hit. As a paladin the Vow of Enmity for the Oath of Vengeance class option or the Sacred Weapon from the Oath of Devotion class option, can reduce the penalty to attack for a short while; and make sure to keep bless up.
Great Weapon Savagery - A half-orc fighter that takes the champion archetype has the potential to do extremely high damage on a more consistent basis with critical hits. For a paladin, the Vow of Enmity allows for a higher chance for a critical hit.

Dual Wielding Weapons

Polearm Mastery
Great Weapon Fighting Style and Polearm Mastery Feat
Great Weapon Fighting - reroll damage on 1 or 2
Polearm Mastery - deal 1d4 damage as a bonus action
Polearms - 1d10 damage
Extra Attack
Viable Classes - Fighter and Paladin
                                     Hit Bonus

Modifier	+0%	+5%	+10%	+15%	+20%	+25%
0	6.75	6.9	7.05	7.2	7.35	7.5
1	8.25	8.4	8.55	8.7	8.85	9
2	9.75	9.9	10.05	10.2	10.35	10.5
3	11.25	11.4	11.55	11.7	11.85	12
4	12.75	12.9	13.05	13.2	13.35	13.5
5	14.25	14.4	14.55	14.7	14.85	15

Duel Wielder
Two-weapon Fighting Style and Dual Wielder Feat
Two-weapon Fighting Style - You deal modifier damage on your off hand
Dual Wielder Feat - Off hand does not have to be light
Battleaxe, Warhammer, or Longsword - 1d10 damage
Viable Classes - Fighter and Ranger

                             Hit Bonus

Modifier	+0%	+5%	+10%	+15%	+20%	+25%
0	6.75	6.9	7.05	7.2	7.35	7.5
1	8.25	8.4	8.55	8.7	8.85	9
2	9.75	9.9	10.05	10.2	10.35	10.5
3	11.25	11.4	11.55	11.7	11.85	12
4	12.75	12.9	13.05	13.2	13.35	13.5
5	14.25	14.4	14.55	14.7	14.85	15

Martial Arts
Monk Martial Arts and Savage Attacks
Martial Arts - attack with off hand as a bonus action (1d4 and 1d6 at level 5)
Savage attacker - Roll Damage twice and take highest
Quarterstaff - 1d6 (1d8 versatile)

                           Hit Bonus

Modifier	+0%	+5%	+10%	+15%	+20%	+25%
0	7.8125	7.9625	8.1125	8.2625	8.4125	8.5625
1	9.3125	9.4625	9.6125	9.7625	9.9125	10.0625
2	10.8125	10.9625	11.1125	11.2625	11.4125	11.5625
3	12.3125	12.4625	12.6125	12.7625	12.9125	13.0625
4	13.8125	13.9625	14.1125	14.2625	14.4125	14.5625
5	15.3125	15.4625	15.6125	15.7625	15.9125	16.0625

Sneak Attack
Rogue Sneak attack and Savage Attacks
Sneak Attack - deal extra damage (3d6 at level 5) with one of your attacks
Rapier and Shortsword/Scimitar - 1d8 piercing damage and 1d6 damage

                             Hit Bonus
Modifier

	+0%	+5%	+10%	+15%	+20%	+25%
0	9.25	10.175	11.1	12.025	12.95	13.875
1	10.25	11.175	12.1	13.025	13.95	14.875
2	11.25	12.175	13.1	14.025	14.95	15.875
3	12.25	13.175	14.1	15.025	15.95	16.875
4	13.25	14.175	15.1	16.025	16.95	17.875
5	14.25	15.175	16.1	17.025	17.95	18.875

Strengths
Polearm Mastery - This option gives you the ability to hit at a further range as well as
Duel Wielder - With an average damage output similar to Polearm mastery, it can deal large amounts damage in larger quantities.
Martial Art Savagery - Like polearm mastery and duel wielder, bonus damage greatly increases the average damage output of this option.

Weaknesses
Polearm Mastery, Duel Wielder and Martial Art Savagery -  All of these option essentially have the same disadvantage which is a smaller amount of damage each turn. Since not all attacks will hit each turn, it may seem that you are dealing less damage.
Sneak Attack - The increased damage from sneak attack relies heavily on your ability to get your sneak attack in. So you will have to stay close to allies or find ways of gaining advantage quite often.

Powerful options
Polearm Mastery - As a paladin choose Oath of Vengence for the damage boosting spells (smite spells and hunter's mark) as well as the maneuverability and synergy from higher level abilities. As a fighter choosing maneuvers that activate on a hit can allow you to use them when its not your turn, allowing for some superior battlefield control.
Duel Wielder - As a ranger, choose colossus slayer and use hunters mark as often as possible for increased damage on each strike, this greatly increases your average damage. As a fighter, the champion archetype will allow for a higher chance to deal critical damage, since you will be attacking more often.
Martial Art Savagery - Taking the Way of the Open Hand increases your battlefield presence as well as giving you better defensive options. Savagery increases damage greatly especially at higher levels.
Sneak Attack Setups - Taking Arcane Trickster can give you a flanking ally (with find familiar) or set you up for a more consistent way to attack with advantage (with true strike).

Conclusion

Considering that normally a character will have something like a 16 ability modifier for their main damage dealing stat we can use that as a base-line for our attack modifier. As well as having the hit bonus at +0%, since we're going to assume no outside help (help from spells or other classes) and an average AC of the creature. We'll then order the highest to lowest damage, on average, for each option.

Highest
13.7 - Greater Weapon Savagery
12.3 - Martial Art Savagery
12.3 - Archery
12.3 - Sneak Attack
11.3 - Duel Wielder
11.3 - Polearm Mastery
10.8 - Greater Weapon Mastery
Lowest

That's all for now. Thank you for reading and please comment if you have any questions or you feel I've made a mistake. Also, if you have suggestions for other topics that you would like to see me write about, please let me know. Have a great day!