Over the last few years there has been a debate in the D&D community about which is better, using two weapons and getting an extra attack or using a single two handed weapon with greater damage dice. On the surface, it appears that in the early development of the character when the fighter has only 1 attack per action, the dual weapon fighter does better overall damage using his bonus action as an attack as well. However at 5th level when fighters get 2 attacks per action, with the dual weapon fighter getting a 3rd attack, the great weapon fighter reaches parity in damage with just 2 attacks. Finally at 11th level when both fighter have 3 attacks per action, the great weapon fighter will produce more damage than the dual weapon fighter. even with the extra attack.
The math is pretty simple, 1d8 of damage averages 4.5 per roll, the dual weapon fighter getting 2 attacks will average 9 points of damage. A great sword does 2d6 damage, which averages out to 7 (3.5x2=7) points of damage per attack. At 5th level the dual weapon fighters average damage becomes 13.5, the great weapon fighters average damage becomes 14 points of damage, pretty close to even. At 11th level the dual weapon fighter's average damage becomes 18. while the great weapon fighters average damage becomes 21 points of damage.
The problem with looking at at like this, is it does not take into account the dual wielder will have more opportunities to do damage over the long term of the game. It is ridiculous to assume both fighters will hit 100% of the time. Just for the sake of argument and to keep the math simple, we assume both fighters are going to hit 75% of the time over 100 rounds of combat and both are 5th level, receiving 2 attacks per action.
Dual Wielding Fighter
3 attacks = 300 Opportunities to do damage
He hits 75% of the time = 225 hits
Each hit is doing 4.5 damage
225 x 4.5 = 1012.5 average damage
Great Weapon Fighter
2 Attacks = 200 Opportunities to do damage
He hits 75% of the time =150 hits
Each hit doing 7 damage
150 x 7 = 1050
Still pretty even, with the great weapon fighter slightly edging out the dual wielding fighter. But lets see what happens when you add in Strength bonus for for each attack. Assuming a Strength of 16 for each fighter, this is an additional +3 damage per hit, this increases the average damage output for the dual wielding fighter from 1012.5 to 1687.5 and increases the great weapon fighter from 1050 to 1500. Now the dual wielding fighter is edging out the great weapon fighter by 187.5 points of damage.
I can hear everyone screaming now, that in order to achieve the dual wielding fighter must take the Dual Weider feat in order to use 2 long swords and if this is the case, the great weapon fighter should get the Great Weapon Master feat, which allows him to take a -5 penalty to hit to gain a +10 to damage, which would be an overwhelming advantage. Except not necessarily, taking a -5 to hit, means the great weapon fighter is reducing the number of times he hits by 25%, so in our scenario, he is going to hit 50% of the time, or 100 times over 100 turns. 17 damage over 100 turns would be 1700 points of damage, only 12.5 more points than the dual wielder. So even under these circumstance, they are still pretty much in parity.
Now lets look at 11th level, when both fighters have 3 attacks per action. The dual wielder will hit 300 out of 400 attacks will produce 2250 points of damage over 100 turns. The great weapon fighter will hit 150 times out of 300 attacks and will produce 2475 points of damage, at this point he is exceeding the dual wielding fighter by 225 points on the average.
So yes, at lower levels, dual wielding is better than great weapon fighting. In the mid levels, both styles are in parity. However at high levels, the great weapon fighter takes the lead by about 10%.
So would this stop me from playing a dual wielding fighter? Fuck no, dual wielding is cool and sometimes cool is better than munchkin. Is a 10% advantage in damage output really a huge advantage, well yes it is, when you consider that you will probably be playing more games getting from 11th level to 20 level than you will getting from 1st level to 11th and really, there is not much stopping you from doing both when it suits you.