As we're deep in the maths here, quick question......
I've just been running out some numbers and I'm getting something really fantastic falling out of them. And I'm convinced I'm missing a variable......
Right so we are comparing 2 Fighters at level 11
SeB) Sword & Board: Duelist Fighting Style, Shield Master, Longsword+2 with +1d6 Fire
Vs
GWen) Greatsword: GWF, GWM, Greatsword+2 with +1d6 Fire
Both have 20 STR. Both have Crit = Dam x2.
So using 100% hit then the damage per attack (with the +10 from GWM and +5% for extra attack from GWM on a crit):
SeB = 17 (Ave Weapon+Fighting Style+Strength+Weapon Bonus+Ave Bonus Damage = 4.5+2+5+2+3.5)
Gwen = 30.27 (Ave Weapon+Fighting Style+Strength+Weapon Bonus+Ave Bonus Damage + GWM = 7+1.33+5+2+3.5+10) x 1.05
OK - now here's where it gets interesting. While Gwen can use GWM if she chooses, Seb can make a Shove Attack as a bonus action. If he succeeds he gets advantage on his attacks (Prone attacker). This does 2 things: Doubles Crit chance, and adds roughly 3.5 to the attack.
Making an (Incorrect) Assumption that Seb suceeds his Athletics check every time, something interesting happens when you look at who does more damage Vs AC (11-22)
11: Gwen+30%
12: Gwen+22%
13: Gwen+15%
14: Gwen+8%
15: Gwen+1%
16: Seb+6%
17: Seb+13%
18: Seb+22%
19: Seb+32%
20: Seb+44%
21: Seb+59%
22: Seb+79%
So here we have confirmation that at AC15, the damage difference between Gwen and Seb equalizes. Either side the Damage bonuses diverge at roughly the same rate.
And even if you bang this up to level 20, Damage equalisation occurs at only AC16. (NB: if you drop it to level 1 with no bonus weapons, damage equalises at AC13)
OK - So now lets recorrect for that Shove contest. Now due to the way Monsters and skills are designed, A Fighter trained in Athletics is hardly ever going have a negative check on a contested Athletics, and is likely to have a much higher score. But even if we give them an equal chance, because of the lack of difference between damage output with attack and without, overall damage drop is minimal.
The outcome? Even with equal Athletics rolls Seb and Gwen's damage equalises only 1 AC later (16), AND Gwen's Diverging Damage bonus flattens out (It's still only +35% at AC11)!
Now obviously there are some stipulations here as the weapon matters, but again that's evenly spread. The higher the bonus to attack, the more it benefits Gwen. The More Bonus Damage, the more it benefits Seb.
Therefore - playing about with the sliders of level, Weapon Bonus, weapon damage, and Monster Athletics score - I can only conclude that for a flat DPS choice for a Fighter, Duellist with SM is Just as good as TWF with GWM, if not better......
OH - I forgot. Plus you have a higher AC, a bonus to Dex saving throws AND Evasion.....
OK - I must be missing something, Right?
(oh and if anyone wants the spreadsheet and macros let me know)