So lets assume a Human(variant) array fighter 6th level. Important ability scores Str & Con start at 16's.
Build 1. (Sword & Board - Dual Wielder)
Feats: dual wielder, tavern brawler, ability score increase 18 strength.
Fighting Style: two-weapon fighting
Attack action: 2 attacks +7 hit, d8+4 damage each
Bonus action: shield attack +7 hit, 1d4+4 damage
AC: 19 (16 +2 +1) chainmail + shield + feat
Build 2. (Two Weapon Fighter)
Feats: dual wielder, ability score increase x2 for 20 strength.
Fighting Style: two-weapon fighting
Attack action: 2 attacks +8 hit, d8+5 damage each
Bonus action: sword attack +8 hit, d8+5 damage
AC: 17 (16 +1) chainmail + feat
Build 3. (Shield Master)
Feats: shield master, ability score increase 20 strength
Fighting style: defense
Attack action: 2 attacks +8 hit, d8+5 damage (most likely made with advantage)
Bonus action: shove attack that if successful gives both of your attacks and any allies attacking target in melee before it goes advantage.
AC: 19 (16 +2 +1) chainmail + shield + fighting style
Build 4. (Stick Beater)
Feats: polearm master, ability score increase 20 strength
Fighting style: dueling
Attack action: 2 attacks +8 to hit, d6+7 damage (staff used one handed d6 +2 fighting style)
Bonus action: attack with staff +8 hit, d4+7 damage
Most likely a reaction attack every now and then for a +8 hit, d6+7 damage
AC: 18 (16 +2) chainmail + shield
I guess what I am getting at is that while the first build and what this thread is discussing is interesting and a good build for a character, there are other great options. Doing the two-weapon fighting thing with the shield has the cost of other options, it basically takes 2 feats to work duel wielding and tavern brawler, there are other ways to get a bonus action attack and gaining your strength modifier to damage, and the shield master feat is very nice even if the shove attack doesn't do damage.