The Caped Crusader vs. the Purple…um…android. Speaks for itself. (Literally and metaphorically).
Weapons: Batman has Batarangs and tons of high-tech weapons in his belt, not to mention his cape/wings. For this fight, he does not have his Batmobile as that would be too much of an advantage. Vision has superhuman strength thanks to his density manipulation and can project a beam of energy from the Mind Stone someone stuck in his forehead. These are very different types of weapons for fighting very different types of bad guys, but both are very effective.
Defenses/weakness: The Dark Night has a nearly impenetrable suit, and can use his cape/wings as a shield. Vision is made of vibranium and can manipulate his density to be nearly indestructible. He can also phase through just about anything. Vision is better here by far, but he has one weakness. More on that later.
Skill: Batman is trained in and masters 127 forms of combat, which he uses to take down lunatic super-villains regularly. Vision is also very skilled with his powers, which is due partly to his programming, but the Dark Night has an edge here.
Mindset/intentions: Batman is fueled by a passive rage at crime in general for the murder of his parents. Once he sets his mind on something, he will get it done. Vision can be somewhat disoriented at times due to only having existed since Age of Ultron, and while he knows what he’s doing, he isn’t entirely sure of the purpose of is existence, not to mention his intentions. Batman easily wins this category.
Use of surroundings: Batman is good at this, but Vision tends to rely on himself and his powers in battles.
Both can fly, but that’s where the similarities end. Vision is powerful and strong, but untested. Batman, media’s most famous detective who has all of DC Comics (Detective Comics) named after him, has been in the game since his childhood. Again, power is up against experience, but this time the newbie is so powerful that even the legendary Bruce Wayne would have trouble staying alive even in his armor, not to mention winning. He will have trouble when his nemesis tries to blow him away with the energy beam. His Batarangs will be useless because of Visions fazing. His armor would protect him from being crushed under Vision’s density, but it wouldn’t stop him from being hurled around by a vibranium android with no intention to let him live. He can use his training and hit home, but Vision wouldn’t even budge. The Caped Crusader has finally met his match.
But Batman has a chance. When Vision reaches a certain density, he is unable to move. Until he lowers his density, Batman can just pluck the Infinity Stone right out of his forehead and take Vision’s power with it. I have absolutely no idea how he would be able to force Vision to take on such a density, but he’s the Dark Night; he’d figure something out. Maybe.
But probably not. Vision would beat the crap out of Batman, and there is not much he can do to use Vision’s weakness against him. As much as I hate to say it, Vision wins. RIP Bruce.