Personally I house rule Two Weapon Fighting Style to allow Extra attack to apply to the bonus attack in place of the +ability mod.
Comparing GWF to TWF:
1 attack: 2d6+Mod vs 2d6+Mod: +1.3333333... to GWF
2 attacks: 4d6+2*Mod vs 4d6+Mod: +Mod+2.666666... to GWF
3 attacks: 6d6+3*Mod vs 6d6+Mod: +4+2*Mod to GWF
As you can see, GWF still wins.
But compare New to Old:
No Extra Attack: 2d6+Mod vs. 2d6+2*Mod: Old wins by a whole Modifier. But this is unlikely unless your a Rogue, in which case it's insignificant vs getting an extra shot at Sneak Attack anyway.
Extra Attack (1): 4d6+2*Mod vs. 3d6+3*Mod: 14 vs 10.5+Mod: Old wins if your mod is >3.5 and you have no on-hit.
Extra Attack (2): 6d6+3*Mod vs. 4d6+4*Mod: 21 vs 14+Mod: Old wins only if your mod is >7. Good luck.
Extra Attack (3): 8d6+4*Mod vs. 5d6+5*Mod: 28 vs 17.5+Mod: Old if your mod is >10.5
Also look at it thematically: You go Two-Weapon Fighting because you want to be a blur of blades. The new way is. The old way... isn't.
Comparing GWF to TWF:
1 attack: 2d6+Mod vs 2d6+Mod: +1.3333333... to GWF
2 attacks: 4d6+2*Mod vs 4d6+Mod: +Mod+2.666666... to GWF
3 attacks: 6d6+3*Mod vs 6d6+Mod: +4+2*Mod to GWF
As you can see, GWF still wins.
But compare New to Old:
No Extra Attack: 2d6+Mod vs. 2d6+2*Mod: Old wins by a whole Modifier. But this is unlikely unless your a Rogue, in which case it's insignificant vs getting an extra shot at Sneak Attack anyway.
Extra Attack (1): 4d6+2*Mod vs. 3d6+3*Mod: 14 vs 10.5+Mod: Old wins if your mod is >3.5 and you have no on-hit.
Extra Attack (2): 6d6+3*Mod vs. 4d6+4*Mod: 21 vs 14+Mod: Old wins only if your mod is >7. Good luck.
Extra Attack (3): 8d6+4*Mod vs. 5d6+5*Mod: 28 vs 17.5+Mod: Old if your mod is >10.5
Also look at it thematically: You go Two-Weapon Fighting because you want to be a blur of blades. The new way is. The old way... isn't.
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