OK, When considering a match-up for this contest I was going to match Batman vs Captain America (Cinematic Universes) but the MCU version of Cap is way stronger than peak human so that's not a fair match-up.
I'd rather match-up two peak-human condition characters who are masters of multiple fighting styles. Both wear specialized body armor with customized gadgets and have no "Super" powers.
Both are Rich: Bruce Wayne is a multi-billionaire, owner of Wayne Industries and T'Challa is the King of Wakanda, with wealth in the Hundreds of Billions and a monopoly on the metal-ore known as Vibranium.
Both have lost a parent Violently. Bruce Wayne lost his Mother & Father to an armed robber in a dark alley behind a Theatre. He was a young child and it changed his life forever. It was the formative moment that created Batman.
T'challa's Father (T'Chacka) was killed by a rival to the Throne of Wakanda. T'Challa swore to avenge his father and Assume the throne as the rightful heir and Ruler of Wakanda. When he assumed the Throne he became the Black Panther, a title that was handed down through the generations.
Both are Masters of Hand-to-Hand Combat. Batman studied with The League of Shadows, learning to use swords, throwing weapons and vicious take-downs. In China, he learned all the Animal styles of Kung-Fu. With the League, he learned the art of Concealment, to hide in the Shadows and become a Shadow himself.
Black Panther was raised as a Warrior from childhood. He trained his entire life, learning to Hunt, to Track to Conceal in the heavy forests and grasslands in and around Wakanda. He learned to fight, to Kill and to defend his homeland from outside invaders. Spears, Throwing Weapons and Vibranium claws in his Gauntlets are his main weapons. He is Agile and Brutal.
So here we go...
Batman vs Black Panther. Who would Win?
Batman arrives in what appears to be an abandoned Warehouse, looking over the scene with his Detective Mode lenses, which are built into the eyes of his helmet.
Amid the pallets of crates marked "Wakanda" he sees a strange distorted blur. He tries to make out the silhouette but it seems as if the shape is absorbing the sonar emitter of his suit.
The silhouette laughs loudly at Batman, proclaiming proudly- "Your Sonar gives you away like a Beacon Batman!" He laughs again as Batman glides down to the main floor using the electrostatic charge to make his cape rigid.
"Impressive Armor you have, Batman," continues Black Panther emerging from the darkness behind the pallets. "Did you make it yourself?"
Batman's only answer is a low growl "Who are You?"
"Who am I?" repeats Black Panther laughing again "I am your Better," he adds while vaulting forward to strike at Batman's chest. Batman jumps back, narrowly evading the Vibranium Claws of Panther's gauntlets. Batman calculates quickly that this man has incredible speed and military training. His suit looks to be composed of some unknown metal that deflects and absorbs energy waves.
Batman dodges another swipe while taking out an EMP Batarang. He throws it at the head of his opponent who back-flips incredibly out of its' way. As Panther flips he kicks Batman full in the face with his armored feet. The blow stuns Batman momentarily as he too hits the floor, putting his weight on both hands as he spin kicks, sweeping Panther as his hands hit the floor.
Panther lands hard on his back before leaping up on his haunches. Batman swings his cape in a whipping motion at Panther, catching him full in his masked face. Panther grabs the cape with both hands while kicking Batman full in the abdomen, the force knocking the wind out of Batman. He recovers quickly, slamming downward with his right arm to get his cape out of Panther's hands. He then fires the spikes out of his forearm and gauntlet. The spikes hit Panther hard but deflect off his mask and chest. The two opponents quickly fall back from each other, trying to gauge the other's abilities.
Panther laughs again before proclaiming. "I underestimated you Batman... You fight Well for a lazy American."
Batman only scowls before answering- "I'm far from Lazy. That body armor you're wearing is unique, but I've discovered its' weakness... Sympathetic Frequencies," he states, producing a small electronic device from his Utility Belt. He quickly presses the button and a loud ultrasonic and ear piercing shriek emits from the device.
Panther falls to the ground, holding his head and trying to stop the painful sound as it continues. He pulls off the mask, revealing the handsome features of the King of Wakanda- T'Challa.
Batman approaches quickly, still holding the device. "Had enough your Majesty?" he asks, recognizing the King of Wakanda. T'Challa nods his head painfully, blood trickling from his nose.
Batman turns off the device before extending a hand to him. T'Challa accepts it. "It's obvious you and I should be Allies... Not Enemies," adds Batman, helping him up.