I might generally be down on complexity in role-playing game mechanics, but I do enjoy running the numbers.
Here’s one comparison of three fighting styles in D&D5e. Caveats: This is based only on the PHB (as it is the only book out when I’m writing this). I’ve chosen a very specific situation to analyze; there may be no generalizations to make. This is only about averages; once you’re rolling dice, anything can happen. This doesn’t consider tactics and such. Also, there’s every possibility I made a mistake.
Huey, Dewey, and Louis are triplets. They’re all 1st level fighters with 16 (+3 modifier) strength, 14 (+2 modifier) dexterity, and 15 (+2 modifier) constitution. They each have 12 hp. They’ve all got “chain mail” (AC 16) armor. Their proficiency bonus is +2.
(The “chain mail” doesn’t let them use their dexterity bonus for AC, but they got it as part of the starting equipment. The only armor that would give them a better AC would be half plate, but they can’t afford it.)
Huey has chosen the Defense fighting style (+1 AC), a war pick (d8), and a shield (+2 AC). His AC is 19.
Dewey has choosen the Two-Weapon Fighting style (add ability modifier to off-hand attack damage) and two shortswords (d6). His AC is 16.
Louis has choosen the Great Weapon Fighting style (reroll damage rolls of 1 or 2) and a maul (2d6). His AC is also 16.
They’re going to have a little tournament among themselves. (They’ll use the “Knocking a Creature Out” rule to keep from killing one another.) Since they all have the same number of hit points, their chance of winning a bout can be determined by comparing their average damage per round versus their opponent’s AC.
Bout 1: The odds favor Dewey (4.9 average points of damage per round) over Huey (3.975).
Bout 2: The odds favor Louis (4.383) over Huey (3.975).
Bout 3: The odds favor Dewey (6.85) over Louis (6.083).
So, Dewey with his two shortswords is favored in two of the three bouts. Huey with his war pick and shield is not favored in any.