Rock... Panther... Bat... SQUISH!

      No, rock, paper, scissors won't solve this battle - but neither will it be as easy for Batman to defeat the Black Panther as it was easy for him to defeat the Green Lantern - of course Guy Gordon thought he could easily defeat Batman by taking off his ring - he was out in one punch.  I would be remiss in my argument if I did not allow that Batman was indeed a worthy opponent for the Black Panther, but the Wakanda native has the knowledge, the patience, the skills, the armor, and the extra help of magic to defeat the Batman in any situation.
       Since T'Challa became the chieftain of his tribe, he learned many skills - he is a master at martial arts, having learned advanced fighting both in hand-to-hand combat and with weapons.  As a superior gymnast, he is extremely flexible and has the ability to move like an animal or a man.  Batman is indeed skilled in martial arts, but the quickness and deftness with which the Panther moves together with his unusual fighting style, he would have Batman on the ground in seconds.
       As the eventual chieftain of Wakanda, T'Challa was taught by his father to "think two steps ahead of his enemies and three steps ahead of his friends." He would know that Batman prepares well for his battles and will have done his homework.  Batman's weaknesses come from two things - his inability to work well as a member of a team and the unfortunate habit of taking everything personally.  Panther would know that the key to defeating Batman lies in a mind game as well as in the ability to distract his opponent.  Using his form of martial arts and magic which he developed and perfected, Panther would wear the Bat down before he ever had to worry about coming in direct contact with him.
       In addition, Panther has been taking a special heart-shaped herb that allows his senses and physical attributes to develop to their peak performance.  He has near-superhuman strength and senses.  This further enhances his hunting and tracking abilities.  He's known for being able to remain unseen if the situation requires it.  He has worked in large cities, such as New York, and in the wilds of Africa he learns to adapt quickly to his environment.  Batman rarely fights out of Gotham City - even the battle with Captain America was on the Bat's home turf.  Panther would not have a problem with this due to his extensive research and sensory perception.
       Many people argue that Bruce Wayne is a genius and this puts him to the advantage in most situations.  The Black Panther is regarded as one of the eight smartest people on the planet and holds a Ph.D. from Oxford University.  His intelligence allows him to work with the components of vibranium the hardest metal known to man.  This is what Captain America's shield is made of and, consequently, T'Challa made a suit of vibranium for himself which he wears to fight in.  Harder than Batman's suit, but just as flexible, Panther can deflect anything that Batman has to throw at him - whether his technology revolves around knives, bullets, or bombs.
       But Panther isn't without his own weapons.  He wields a set of retractable vibranium claws.  They aren't part of him like Wolverine's, but they are sharp.  He is skilled with special throwing claws - also made of vibranium - and with sticks, swords and his tribe's advanced weaponry.  He has access to money through the vibranium owned by his country and has access to the resources that Bruce does.
       Batman was defeated by two people: Bane and The Bronze Tiger.  Bane broke Batman's back through sheer strength, wearing him down.  The Bronze Tiger was simply better at martial arts than the Bat was.  The Panther's skill, caution, and adaptability give him the upper hand significantly.  He also has access to the ancient power of the African Panther deity.  He uses the magic from the god to help enhance his own abilities, making him stronger, faster, and more cunning.
       Even given access to all of his traditional resources, there is no way that Batman could defeat the Black Panther.  Bruce Wayne is clever, but he lacks experience outside of Gotham city.  He lacks adaptability to other terrain and has to have the upper hand before he ever gets in a fight or he's lost it.  Panther's preparedness gives him the ability to duke it out in any situation but also the mental preparedness to understand and know his enemies.
                   Is it just me?
                         Or was that a Bat hitting the floor?