Yeah, it seems kinda weak and fiddly now.
That's a good point. I was focused on how bad this was for greataxe-wielders, but it's pretty lame even for greatsword/maul-wielders. An average increase of 1 1/3 point of damage on a roll of 2d6 (which is the best case scenario for this ability) doesn't compare well to the Dueling Fighting Style.
EDIT: I should note that the extra damage from Great Weapon Fighting gets doubled on a crit while the +2 damage from Dueling doesn't, but still.
I don't quite understand your analysis.
Dueling gives you +2 damage on a max D8 weapon.
Great Weapon gives you reroll 1 or 2 on a max D12 or 2D6 weapon.
So the first one is D8+2 or 6.5 average points of damage (pre-Str) which is 2 points of damage over someone who does not have this ability.
The second one is the equivalent of D10+2 or 7.5 avarege (1 extra point over 6.5 of D12) or the equivalent of 2D4+4 (2 extra points over 7 of 2D6)
Dueling: Going from 4.5 to 6.5 damage vs.
Great Weapon: Going from 6.5 to 7.5 damage with a D12 weapon (or going from 7 to 9 points with a 2D6 weapon)
Yeah, the Greataxe only gets one extra point of damage compared to dueling getting 2, but it still does more overall average damage, especially on a crit. The dueling weapon guy gets to use a shield. Pros and Cons.
The real potent fighter is the two-weapon fighter with a short sword in each hand doing D6+2 in each hand (pre-Str). He averages 11 points of damage plus 2x Str mod if both hit. And if he downs a foe with one attack, he can still attack another foe with the off hand attack. Lot of love there.
Granted, once Fighters gets Extra Attack at level 5, it becomes 9+Str plus 9+Str for the Greatsword wielder and 5.5+Str plus 5.5+Str plus 5.5+Str for the two short sword wielder. The two handed wielder starts to catch up and actually passes the two weapon wielder at level 11. But, that's balanced. The one fighter style was better at levels 1 to 10, the other style better at levels 11 to 20. Criticals affect this as well, but the two weapon wielder gets slightly more criticals on average which helps.