Since a lot of people have asked the question, lets look at the math. Between GWF and TWF...is either one strictly superior?
All situations are compared against a AC 16 character.
Note: DPR = Damage Per Round.
1st Level Fighter, with no fighting styles of note (they took that sweet +1 to AC!)
Str: +3, Prof +2.
TWF: 2 d6 weapons. DPR: 5.35
GWF: 1 2d6 weapon. DPR: 5.35
Winner: Tied.
This one is a complete tie. Both style do the same damage, even if you modify the beginning strength. It depends on whether you want your damage in small chunks with better to hit, or a massive attack that misses more often. Considering the potential for damage overkill (and the fact that sometimes you just need to hit) I would give the slight edge to TWF, but its really a style preference.
1st Level Fighter, using the various fighting styles
Str: +3, Prof +2.
TWF: 2 d6 weapons. DPR: 7.2
GWF: 1 2d6 weapon. DPR: 6.5
Winner: TWF
The TWF fighting style provides more damage and a greater chance to hit. It is strictly the superior choice at the early levels.
8th level Fighter, no fighting styles
Str: +5, Prof +3. Crit on 19-20. 2 attacks as base.
TWF: 2 d6 weapons. DPR: 14.375
GWF: 1 2d6 weapon. DPR: 17
Winner: GWF
As the number of attacks increase, TWF's one bonus attack starts to make less of an impact.
8th level Fighter, with styles
Str: +5, Prof +3. Crit on 19-20. 2 attacks as base.
TWF: 2 d6 weapons. DPR: 17.63
GWF: 1 2d6 weapon. DPR: 18.99
Winner: GWF
The difference is a little less now, as the TWF fighting style ultimately does more good than the GWF one does. However its not enough to overcome GWF damage advantage.
A quick look at the cleric and rogue
Bonus damage that applies on both or either attacks always favors the style with more attacks. As such, the clerics divine strike (and buff spells that affects their attacks) and the rogue's sneak attack favor TWF straight up. Because these class do not get extra attacks like the fighter, GWF never gets a chance to come back in terms of damage.
In summary, optimal play for damage
Fighter (1-4): TWF with style
Fighter (5-20): GWF with style
Cleric (1-7): Either style...unless using certain buff spells.
Cleric (8-20): TWF
Rogue (1-20): TWF with sneak attack
All situations are compared against a AC 16 character.
Note: DPR = Damage Per Round.
1st Level Fighter, with no fighting styles of note (they took that sweet +1 to AC!)
Str: +3, Prof +2.
TWF: 2 d6 weapons. DPR: 5.35
GWF: 1 2d6 weapon. DPR: 5.35
Winner: Tied.
This one is a complete tie. Both style do the same damage, even if you modify the beginning strength. It depends on whether you want your damage in small chunks with better to hit, or a massive attack that misses more often. Considering the potential for damage overkill (and the fact that sometimes you just need to hit) I would give the slight edge to TWF, but its really a style preference.
1st Level Fighter, using the various fighting styles
Str: +3, Prof +2.
TWF: 2 d6 weapons. DPR: 7.2
GWF: 1 2d6 weapon. DPR: 6.5
Winner: TWF
The TWF fighting style provides more damage and a greater chance to hit. It is strictly the superior choice at the early levels.
8th level Fighter, no fighting styles
Str: +5, Prof +3. Crit on 19-20. 2 attacks as base.
TWF: 2 d6 weapons. DPR: 14.375
GWF: 1 2d6 weapon. DPR: 17
Winner: GWF
As the number of attacks increase, TWF's one bonus attack starts to make less of an impact.
8th level Fighter, with styles
Str: +5, Prof +3. Crit on 19-20. 2 attacks as base.
TWF: 2 d6 weapons. DPR: 17.63
GWF: 1 2d6 weapon. DPR: 18.99
Winner: GWF
The difference is a little less now, as the TWF fighting style ultimately does more good than the GWF one does. However its not enough to overcome GWF damage advantage.
A quick look at the cleric and rogue
Bonus damage that applies on both or either attacks always favors the style with more attacks. As such, the clerics divine strike (and buff spells that affects their attacks) and the rogue's sneak attack favor TWF straight up. Because these class do not get extra attacks like the fighter, GWF never gets a chance to come back in terms of damage.
In summary, optimal play for damage
Fighter (1-4): TWF with style
Fighter (5-20): GWF with style
Cleric (1-7): Either style...unless using certain buff spells.
Cleric (8-20): TWF
Rogue (1-20): TWF with sneak attack