So, while there's a lot of drama at the corporate level, I think most of us have very affectionate feelings toward 5th Edition as a mechanical gameplay system. Yes, there are some who will say that other systems are better (I think in matters of taste there is rarely anything that is strictly "better" than others) but I don't feel any qualms getting into the crunchy nitty-gritty.
Fighting Styles are options that Fighters, Paladins, and Rangers automatically get at either level 1 (Fighters) or level 2 (Paladins and Rangers). College of Swords Bards also get some of these options, and in One D&D, it looks like all three Warrior classes (Fighters, Monks, and Barbarians) will get access to them. In the latter case, we don't have a full picture of all the Fighting Styles, though the ones we've seen look pretty similar to what exists in 5E.
What I wanted to take a look at was the relative values of all these styles. I suspect that the potency can be surprising.
We'll start with those available to the Fighter, which covers most of them, and then take a look at the ones that only the Paladin or Ranger can get (which I think might be just one each).
Archery:
This is one of the most straightforward ones. You get a +2 bonus to your attacks with ranged weapons. So, how do we evaluate the power of this fighting style?
Ultimately, what it means is that whatever your percentage chance to hit with your ranged attacks increases by 10%. Let's say you have a +3 to Dexterity and a +2 Proficiency Bonus. That means that hitting a target with an AC of 16 will happen 50% of the time (11-20 on the d20). This fighting style increases that chance to 60% of the time.
I don't know that I want to go through the total math of the implications for that overall on your damage output, but overall just being able to hit with your attacks more often is going to be very good for you. So, while simple, I think this is a very strong choice if you're going to be a strongly ranged-focused character.
Let's imagine, just as a scenario, that you're a level 5 Dex Fighter with a nonmagical longbow. At this level you have 18 Dexterity (+4) and you're trying to fight a target with an AC of 18.
Without this fighting style, you will hit the target on an 11 or higher for 1d8+4 (8.5 damage on average) and crit on a 20 for 2d8+4 (13). That means 45% of the time you're dealing 8.5 damage and 5% you're doing 13, and 50% of the time you're doing 0. So, we get an average damage per attack of 4.475, doubled by your two attacks to 8.95 per turn.
With the fighting style, you're now hitting on a roll of 9 or higher, meaning you get a 55% chance to get your standard damage. That gives you an average damage per attack of 5.325, doubled to 10.65, meaning we've increased our damage per turn by 1.7.
That's honestly a little underwhelming, to be honest, though I think you could argue that any feature that lets you tack on things after you hit (such as a battle master's maneuvers) could bump this up significantly. There's also potentially a larger difference in the case of very high AC monsters and very low.
Blind Fighting:
This one's hard to evaluate on its own. The key, I think, is that characters could work synergistically to make this very potent. If you have a Warlock (with Devil's Sight) drop Darkness on the battlefield, and you have Blind Fighting, you could really wreck house together against a bunch of blinded enemies.
Indeed, this could serve well in non-combat situations as well.
Ultimately, this is situational, but in a common enough situation that I think it's a great choice (though probably for only for melee builds given its short range - 10 feet of blindsight is not going to be great for an archer.)
Defense:
This adds one point of AC if you're wearing armor. Like Archery, this is going to have a varying impact based on your own base AC and the hit bonuses of the things you're fighting. My Eldritch Knight took this as part of his quest to get an insanely high AC (this, a +1 shield, and plate put him at 22 and then he had the Shield spell to bump it to 27).
The value of this is also going to depend heavily on how many attacks you take in a round - if you're positioned to be the true tank and are getting attacked by multiple enemies, the benefit here has a real multiplier.
I will note, though, that if you're willing to spend 1500 gold on plate armor, this essentially makes Split into Plate and Chain Mail into Splint, so it's worth considering. It's also the only fighting style (except, situationally, Blind Fighting) that increases your own personal survivability.
Dueling:
The math here is pretty simple: you get two more damage per hit with an attack. If you have a longsword, you're now actually better off just using it with one hand.
Indeed, while 2 damage per hit might not seem like a lot, with multiple attacks this actually winds up being a pretty significant bonus - a flail, say, with +3 to Strength goes from 1d8+3 to 1d8+5, or 7.5 to 9.5 on average - a 27ish% increase.
Great Weapon Fighting:
On this, the math is somewhat more complicated but not by a ton. This allows you to reroll (once) 1s and 2s with any melee weapon you're wielding with both hands. Effectively, then, the way you can figure out the average damage for any die you're rolling is to first figure out the normal average (3.5 for a d6, 6.5 for a d12, etc.) and use that in place of 1 and 2 when adding up all the potential results. So, for example, our average d6 roll (such as with a Maul) would be (3.5+3.5+3+4+5+6)/6, which comes to 4.167 (4 and a sixth).
Thus, with 2d6 as the damage dice, a Greatsword or Maul goes from 7 average to 8.33, bumping damage for the dice alone by about 19%. When we account for Strength (let's look at a base of +3) that means 10 damage becomes 11.33, for a bump of 13% more damage.
Now, this will affect crits in a way that Dueling does not. Jeremy Crawford has said this is meant to only apply to the damage of the weapon itself, and not secondary effects like Divine Smite or Battle Master Maneuvers (or even Improved Divine Smite). I'd argue that in that case, while this is the only fighting style that pushes for maximizing damage with the hardest-hitting weapons in the game, it falls short of being really exceptional. However, if you home-rule it (like I do) to work with those other damage sources, it starts to look more appealing.
For instance, my Paladin has a +2 Greatsword. If she smites against a vampire spawn (she's in a Curse of Strahd campaign) at 2nd level, that hit would do 2d6+7+4d8. Without this, the average damage there would be 7+7+18, or 32 total.
With this, the 2d6 is now an average of 8.33, and the d8s are now going for 5.25 each, so the smite is now 21 damage, giving us a total damage of 36.33, which is... ok, it's 13% more damage.
Dang, maybe this fighting style just isn't that good?
Interception:
This is a fighting style I slept on until I saw both of our Paladins in our Wildemount campaign take it. And holy crap, folks. With this style, you can use your reaction to interpose a shield or melee weapon when another person within 5 feet of you is hit with an attack, reducing the damage of that attack by 1d10 plus your proficiency bonus.
Now, let's consider what this effectively means: on average, that's 5.5+PB, so at level 5, it's 8.5 damage reduced on average.
Another way to think about it: you get a potentially more powerful cure wounds as a reaction every single turn as long as you use it immediately.
Our party does not have a Cleric or a Druid or a Divine Soul Sorcerer, but our tactics are typically to have the two wizards far outside the fray (it's not a balanced party) or for us to each huddle up with a paladin. The number of hits that have been utterly negated by this fighting style is high. And even just reducing a hit from, say, 10 damage to 3 makes it a far less scary encounter.
Now, this will lose value as you start fighting creatures that hit harder (we'll compare it with the next one,) but this is still potentially a huge amount of damage negation without really any serious limitation on its use. I think this is a top-tier fighting style.
Protection:
The older cousin of Interception, this works similarly except it requires a shield (can't use this is you've got a two-hander) and rather than reducing incoming damage, this imposes disadvantage on the attack.
The math of advantage and disadvantage is complicated, but one of the issues you can have with this is that it might wind up not really doing anything - if the monster rolls two high rolls or two low rolls, you haven't really changed anything (you can ruin a sneak attack, potentially).
In theory this should be more useful if the monster is hitting so hard that 1d10+PB isn't really a significant chunk of the damage, but I think Interception is probably better than this in most cases.
Superior Technique:
I'd actually forgotten this exists. This basically lets you use a Battle Master maneuver once per rest, with a d6 superiority die to fuel it. Oddly, this might actually be best on a Battle Master, because I think you can use the maneuver you learn with this style using your other superiority dice.
I'd also consider taking this and Precision Attack if you are going with the Great Weapon Master or Sharpshooter feat, and thus potentially negate the downside of the -5 element of those feats.
Maneuvers are versatile and useful (and I think it's possible the One D&D Fighter will get them as a base Fighter feature,) making this a potentially exciting option - though it's also a little dependent on how often you take rests in your campaign.
Thrown Weapon Fighting:
This allows you to draw a thrown weapon with each attack, and gives you a +2 bonus to the damage of your thrown weapon attacks.
I think this would be great if there were better support for thrown weapons. The problem here is that past level 4 or so, you're probably looking for a magic weapon that you can use repeatedly. If you have an Artificer (a class that doesn't get Fighting Styles) to give you a Returning Weapon, this could be fun, but I think this is almost never going to be optimal. At most, it makes a thrown-weapon-based character just barely viable.
That, to be fair, is pretty cool. But this is still a big commitment just to be kind of on par with other playstyles.
Two Weapon Fighitng:
The math here is actually pretty simple - this will give you 5 extra damage per turn once your Strength or Dexterity is maxed out. With the One D&D changes to light weapons, dual-wielding looks a lot more viable as a playstyle, though with the 5E rules requiring a bonus action, it's a little more restrictive.
Still, given that we've shown that Great Weapon Fighting only adds 2 2/3 damage per round (with two attacks) and Dueling only adds 4, this starts to look pretty good. The one class I'd really not recommend it on is the Fighter if you plan to go to level 11 or higher, because as that class gets more attacks (not to mention action surge) beyond the normal two, this loses value while things like Dueling and Great Weapon Fighting get better (though even with three attacks, GWF still only gives you 4 more damage per turn).
Interestingly, at least in the 5E rules, Paladins don't get this, despite the fact that dual-wielding on a Paladin (or a Barbarian for that matter) is actually a pretty good choice, thanks to getting more chances to crit (and thus crit-smite) and the bonus damage of Improved Divine Smite.
Unarmed Fighting:
This gives your unarmed strikes a d6 damage die rather than being just 1, and adding Strength as usual. You can also deal 1d4 bludgeoning damage at the start of your turn to a creature you're grappling.
So, this is largely redundant to a Monk, who don't get Fighting Styles in 5E anyway.
This is niche, though while the Thrown Weapon style is not one I think there's much of a build for, you could definitely take this if you wanted to be a really grappling-heavy character. While there's some redundancy with the Tavern Brawler feat, there's also some synergy here, as well as the Grappler feat.
So there you have it. Perhaps in another post we'll compare and contrast this with the One D&D Fighting Style feats and see whether their value rises, falls, or stays the same.
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