Okay, here's some basic numbers for a level STR 18 5 GWM paladin (no smiting) vs. a STR 18 level 5 Shield Master battlemaster (no superiority dice usage). I put the script up here if you want to tweak STR score/number of minotaurs/AC/HP/feats/etc. Because it's a Monte Carlo sim, the numbers could be slightly off compared to the closed-form mathematical solution, but since I ran each combat 10,000 times they should be close enough that you won't notice a difference in play.
http://www.tryfsharp.org/create/maxwilson/GWMFighterCompare.fsx (requires Silverlight; doesn't work in Chrome)
Note four things about this combat:
* My minotaurs do not use their reckless attack. This is a best case for the Shield Master fighter because trust me, when they use it, it's even worse for the shield guy because his AC is worth less and the GWM guy hits more. (I ran the numbers both ways.)
* Shield guy is using his shield to knock prone before making any attacks (granting advantage), and then if there is only one opponent, and that opponent is prone, he is backing away 30 feet. The minotaur gets an opportunity attack on him from the prone position but then cannot attack him next turn (only has 20 movement after getting up), so the net effect is that successful push = minotaur gets disadvantage on next attack.
* I am including bonus action attacks for the GWM guy on a crit or kill. They go towards the next minotaur who is still alive.
* The setup is that he fights N number of minotaurs (e.g. one minotaur at a time, or three minotaurs at a time), and then as soon as that fight is over, fights again and again until he dies. Then I average how long he lasted and how many minotaurs he killed before dying.
// Shield Mastery fighter vs. 1 Minotaur not using Reckless Attack
analyze (10000, 18, true, false, true, 1, 7, fun (roll) -> d(1, 8) + 4 + if roll = 20 then d(1,8) else 0)
Average total damage before dying: 204.6, killing 2.1 minotaurs over 19.8 rounds with 10.31 DPR.
// GWM paladin vs. 1 Minotaur not using Reckless Attack
analyze (10000, 16, false, true, true, 1, 7, fun (roll) -> d(1, 12) + 4 + if roll = 20 then d(1,12) else 0)
Average total damage before dying: 267.4, killing 2.6 minotaurs over 16.0 rounds with 16.68 DPR.
// GWM paladin using Power Attack vs. 1 Minotaur not using Reckless Attack
analyze (10000, 16, false, true, true, 1, 2, fun (roll) -> d(1, 12) + 14 + if roll = 20 then d(1,12) else 0)
Average total damage before dying: 412.4, killing 4.0 minotaurs over 18.2 rounds with 22.69 DPR.
// Shield Mastery fighter vs. 3 Minotaurs not using Reckless Attack
analyze (10000, 18, true, false, true, 3, 7, fun (roll) -> d(1, 8) + 4 + if roll = 20 then d(1,8) else 0)
Average total damage before dying: 68.4, killing 0.4 minotaurs over 6.5 rounds with 10.58 DPR.
// GWM paladin vs. 3 Minotaurs not using Reckless Attack
analyze (10000, 16, false, true, true, 3, 7, fun (roll) -> d(1, 12) + 4 + if roll = 20 then d(1,12) else 0)
Average total damage before dying: 87.8, killing 0.6 minotaurs over 5.0 rounds with 17.41 DPR.
// GWM paladin using Power Attack vs. 3 Minotaurs not using Reckless Attack
analyze (10000, 16, false, true, true, 3, 2, fun (roll) -> d(1, 12) + 14 + if roll = 20 then d(1,12) else 0)
Average total damage before dying: 152.1, killing 1.3 minotaurs over 5.9 rounds with 25.92 DPR.
I encourage you to play around with the script if you want to evaluate different levels, but I wanted to highlight two things about the results:
1.) Minotaurs are a particularly bad opponent for the shield guy. He is barely more survivable than the GWM guy (lasts 19 rounds before dying, vs. 18.2 for GWM guy) and he does less than half the damage over that time.
2.) If you ever fight three minotaurs at the same time, it doesn't matter whether you've got Shield Mastery or GWM or Heavy Armor Mastery or what. Just run away because they're going to kill you!