Batman
Abilities
Indomitable Will:
He has no known superhuman powers, but he does have an extreme, almost superhuman "Force of Will".
Intimidation:
Batman has the ability to instill fear in others, even the people that know him best are intimidated by him.
Peak Human Conditioning:
Through intense training, the Batman represents the pinnacle of human physical prowess. His strength, speed, stamina, agility, reflexes and coordination are at peak human perfection.
Martial Arts Master:
Trained by Henri Ducard and the League of Shadows, Batman is a living weapon, having mastered Western forms of both armed and unarmed martial combat.
Weapons Master:
Through his martial arts training, he has become an expert on many types of weaponry. He is an exceptional swordsman as evident in his fight with Henri Ducard.
Master of Stealth:
His training has made him a master at stealth capable of disappearing into the shadows and sneaking up on unsuspecting prey.
Expert Mechanic and Vehicular Driver:
Proficient at combat driving. Has learned improved vehicle designs. Was trained and proficient in basic vehicles operations.
Strength level
Batman engages in an intensive exercise regimen.
Samurai Jack's Abilities
As a boy, Jack has travelled around the world to prepare for his confrontation with Aku, both physically and mentally. Jack visited many civilizations in ancient times, such as China, Egypt, Greece and northern Europe. Everywhere he went, he attempted to master each art of combat from the cultures he met. He trained with viking sailors, Robin Hood, shaolin monks, the Greek olympic contestants and several others. Jack has a complete mastery of sword, staff, spear, bow, and mounted combat, and can also fight unarmed, albeit with limited effectiveness when fighting against robots and cyborgs. Additionally, he is highly adaptable, able to intuitively grasp the controls, potential combat functionality, and weaknesses of highly advanced technology even when first encountering it. Jack is also knowledgeable about the mystic and arcane, though he does not demonstrate the ability to use magic. He is also very good with animals and can befriend them quite easily.
Jack is exceptionally skilled in the martial arts and follows Bushido strictly. After some training with rather large boulders as weights, Jack gained the ability to leap several stories into the air. The forest man who taught him this technique refers to it as "Jump Good." When Jack jumps, he elevates so high that he appears to fly (as stated by Aku). His reflexes are excellent; in fact, he is able to block bullets fired by machine guns with his sword and overwhelm hundreds of opponents at once with sheer speed and skill. He has also been shown to have become skilled in ninjitsu. Even Aku fears Jack, mostly because his sword is one of the few things able to dangerously harm him.
Jack's magic katana was forged by the gods Odin, Ra and Rama through 3 mortal avatars. The sword's main component was the pure spirit of good that humans possess. A portion of this was extracted from Jack's father and then hammered and forged into a katana. It is preserved and maintained by Jack's ancestors and is one of the few weapons capable of destroying Aku. It is incapable of being broken or shattered due to its mystical qualities. The sword is very sharp; once Jack sliced an arrow with a jewel tip in half simply by putting the blade in the path of the arrow. Jack's sword seems to have a mind of its own, as shown when Jack was hunting—it refused to cut down a helpless deer for Jack's consumption. Also, Aku once succeeded in stealing the sword and attempted to kill Jack with it, but he was unable to pierce Jack's skin with it because the sword can't hurt those that are good and pure, although his sword has been known of harming good ones in a few episodes. For example, in the episode about that old model of robots that was given emotions, he was forced to fight the samurai and the samurai destroyed him with the sword. And also the episode were the samurai is infected with Aku's pure evil, he, or rather Aku, uses the sword to attack those reptillian monks. Athough they weren't sliced into pieces, they were clearly hurt by the sword.
It must be noted that in certain episodes, Jack uses abilities that he never uses again (similar to Aku), such as his ability to hide in bright light, seen in episode XL, "Samurai vs Ninja". However, this is more of an artistic effect than an ability of Jack's, as the purpose of that episode was to show his battle against a ninja clad in black clothes. Their fight takes place in a stylized setting of abrupt light and shadow, with Jack showing up against the black background and the ninja becoming visible against the light.