Due to cosmic forces, time warps, worm-holes, or whatever...
The Dark Knight faces the The Jedi Knight of the Dark Side ;

Batman against Darth Vader:
Matches:
*Both are skilled at martial arts
*Both wear a form of [black] body armor, accented tastefully with nifty capes
*Both carry personal sidearms in which they are experts
*Both have really intimidating speaking voices
Special Skills:
Batman has: Superior Fight Strategies; he can judge an opponent's strengths and weaknesses, at a glance, and knows how to use them. Excellent Chess player.
Darth Vader has: The Force; he can telekinetically move large objects with his mind, and if he is allowed to focus without distraction, can use the 'Sith Force Choke'. If he is distracted, he's been known to fall back on the 'Sith Bladder Spasm'.
Shortcomings:
Batman is: Only human, he has his physical limitations as Bruce Wayne, millionaire playboy; sometimes he needs a quick shower, minor surgery, a five-star meal and an expensive, discreet hooker.
Darth Vader is: Too reliant on his power, he lacks patience and finesse, and will charge in like a Bantha in a China shop, while forgetting to charge his exosuit batteries.
Neither can:
* Call for back up- no Super-Friends; no Storm Troopers. This is one-on-one.
* Resort to heavy vehicles- no Batmobile/plane/cycle/boat, etc.; no Tie fighters nor Battle droids.
* Remove cowls/helmets- secret identities must be respected and maintained
* Claim a power/ability they haven't had before- the Fandom Base knows all, sees all and controls all
READY...
GO!