We haven’t seen Batman v Superman and we don’t really have any intention to. However, I can do the general Wonder Woman, Batman, and Superman breakdown using Bruce Timm’s DCAU/Timmverse which is actually just as useful when it comes to studying superhero combat. There’s some good stuff there, especially in Justice League Unlimited where we get a lot of heroes who fight in a variety of different ways.
One of the really cool things about DC’s heroes in comparison to Marvel’s is that the archetypes build to a lot of really interesting combinations which compliment each other well. It’s my personal opinion that Marvel does “Versus” stories better because Stan Lee loved the concept of superheroes beating each other up and because they’re much more neurotic. They’re more likely to get into spats over ideological differences when it comes to the right way to fight crime. Most of the Marvel heroes are very human, they’re more likely to squabble, and those squabble’s are more likely to result in fights which either threaten half the Eastern Seaboard or involve the Punisher trapping Daredevil on a rooftop full of sonic mines.
It might be weird to say that the DC heroes are more than human, but they are. They’re much more mythological, more ideals we aspire to reach. They’re the best of humanity and while they don’t have the same neurosis of Marvel, they’re stories have the potential to be incredibly uplifting when they embrace their origins. It’s a different kind of human, better than human, in some ways transhuman. They’re much better at overcoming the basic ideological pettiness which leave the Marvel heroes squabbling in a ditch.
If the next question is “who do you prefer, Marvel or DC?”
The answer is Dark Horse.
I’m kidding. Well, I’m not. Ghost is bae.
The truth is I actually like them both and I think they both tell very different kinds of stories, but those stories are very interesting in different ways. They both occasionally have identity issues, but when they’re on point then they’re fantastic.
Okay, fighting styles:
Superman: Superman doesn’t actually know how to fight. Unlike Wonder Woman and Batman, he isn’t a trained fighter. Combat isn’t his specialty and this is, in large part, because he’s never needed to learn. He’s Superman. 9/10 he’s invulnerable to most ancillary damage. He’s willing to sit there with criminals and talk it out, mostly because they can’t really do much to him. His powers mean he has an opportunity for empathy in the heat of combat which Batman can’t afford. This is why he generally gets his ass handed to him by the likes of Zodd or other surviving members of the Kryptonian military, or Darkseid. He doesn’t fight so much as flail and again, it’s fine. It makes sense. Superman is also the most emotionally driven of the Golden Trio. While he keeps himself under very strict control most of the time due to the massive collateral damage his powers can cause, he’s the one most easily goaded. There are a number of villains who prey on this flaw including Darkseid and Lex, who both goad him into taking action that have terrible backlash. His powers can be as much as curse as a blessing.
His lack of training and combat knowledge is the main reason why Batman stands a chance against him and why Batman can knock him down a peg. Wonder Woman doesn’t really have the same issues, but it helps anyway.
Batman: Batman is a very clinical fighter, he’s a tactician and a strategist. He’s trained with and been trained by some of the best warriors and hand to hand combatants the DC universe has to offer. Batman’s brain is what lets him keep up though. Of the three, he’s the most likely to see a situation’s hidden trap door or figure out an enemy’s weakness on the fly then determine a solution. He’s the voice of reason to Superman’s emotion, willing to do what’s necessary to make it through but also coming to the battle prepared. Whether that’s carrying a Kryptonite ring in a lead box every time he goes into Metropolis or just having it on standby for twenty years, Batman will always assess the situation before diving in. It’s a good question of how much Batman knows, but really the answer will generally be more than you think.
Batman is the problem solver. He’s the one who most often gets to the heart of what is really going on, sees through the machinations, and figures out why the fight is happening in the first place. The man with the plan is what he is and the best writers like Bruce Timm will recognize that the detective skills actually trump the combat skills. Batman is the Great Detective for a reason. He studies his opponents, attacks their weaknesses, and that’s the path which leads to victory.
Wonder Woman: Unlike the other two, Wonder Woman is actually a soldier. She is a warrior. She understands battle layouts, strategy, and trains with a wide variety of weapons. She can punch properly, she can grapple, and, really, she can fight. I don’t just mean that in the sense she’s classically trained or one of the best combatants in the DCU, but in so much as that’s a part of her outlook more so than Batman or Superman. They aren’t warriors in the same way and Diana can whup both their asses. When in the trio, Wonder Woman is basically the midpoint between Superman and Batman. Unlike Superman, she can actually fight rather than flail. Also unlike Superman, she has existed without all the powers that have essentially been his birthright. While Wonder Woman is physically enhanced via training and magic depending on who is writing the Amazons this week, it’s her enchanted armor forged by Hephaestus that imbues her with her defining superpowers. This gives her the context to human combat and humanity which Superman often struggles with and she has a leg up on Batman in that she’s… well… an emotionally stable adult.
Essentially, she serves as a great balance point between the two extremes of brains and heart. She fights with both without either controlling her actions. Like Superman, she has the luxury of being compassionate toward her enemies and more so than him the ability to control the fight better. Superman is often so strong he can’t really afford to fight at all if he wants to talk someone down, rather he disables them by destroying their weapons or letting him shoot at him until they run out of bullets. Batman, meanwhile, is much more fragile. While, when written right, he’s a very compassionate individual he also has to use his head to stay ahead of the curve in order to get his enemies into a situation where he can talk to them safely. Wonder Woman is the middle ground between the two. She’s a very good tactician and her skill is such that she’s taken on the entirety of the Justice League.
However, her compassion is the balancing strength. For this reason, she has an excellent track record for turning adversaries into allies.
It may not answer the question you wanted, but that’s the best I’ve got.