Batman - Analytical genius and martial arts master who has honed his body and mind to peak human perfection.
Captain America - Master strategist and martial arts master who has above normal strength, speed, reflexes, and agility.
First time fight without Batman preparing for Cap. Then Captain America will win .... BUT....Batman is resourceful enough to survive any fight with someone superior to him and escape.
2nd fight after Batman has analyzed Captain America then the Bat will beat the Cap.