It had to happen eventually.
Batman vs. An Exact Duplicate of Batman
Both are armed with the same equipment and have the same amount of preperation time.
So we can tell the difference, one is wearing the batsuit with the yellow circle around the bat emblem on his chest, the other without.
So, who will win, Yellow Circle Batman or No-Yellow Circle Batman?
Good God. This is like Da Bears vs. Da Bulls.
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Head Explode
No-Yellow Circle Batman would win, because the yellow circle makes the other guy easier to see in a dark room.
Ah Kat, as Batman history teaches us, no oppenent can resist aiming for the yellow circle, under which is an extra thick layer of kevlar armor. With no mesmerizing yellow circle to contend with, Yellow Circle Batman can choose his traget. Like for instance going for the unprotected lower half of the face, something I’m always amazed no one ever thinks to do.
Hmph. An exact duplicate of Batman? You mean someone like Batmanuel?
Are you kidding, Fibber? Have you seen this guy’s chin; the bullet would have a better chance against the kevlar.
I said “exact duplicate” not “cheap knock-off”.
I suggest they settle they realise what’s happened and fight crime together, or go down the pub for a drink (and swap girlfriends). They both win!
Ah, but superheroes involved in an epic struggle cannot “both win”. The resulting paradox would likely tear the DC Universe to shreds . . . for only the what, fifth time in last ten years?
Yellow Circle Batman wins because he calls in Green Lantern for help and tells him No Yellow Circle is a fake. YCB can’t try try the same thing because GL’s power ring won’t work on NYCB’s yellow circle.
But who really wins: AOL Time Warner/Warners Bros. Pictures/DC Comics for milking the idea of B vs. B for all it’s worth in comic sales, movie tickets, TV spinoffs, and merchandising if they know what’s good for them.
Ah, but the current Green Lantern has no yellow weakness.
I’d have specified no outside interference in the OP but I thought that was already obvious to all. Guess I was wrong . . .
Sorry, I’ve been out of comic fanboy circles for a while now, didn’t know, my mistake on both counts.
Given that both Batmans are prepared, we can safely assume that they have both studied the many worlds theory of quantum physics, and invented devices to manipulate them.
Thus, each Batman will use his device to go to the world in which he wins the battle.
Suppose they both sustain the exact same type of wound that Superman received from the Cyborg after Supes came back to life in the Reign Of The Supermen saga . . . the type that burns the emblem off his chest and does no other damage.
Then, with no differnce between them at all anymore, they do that Superman/Doomsday punch-each-other-at-the-same-time thing, both winning and losing to each other at the same time.
And no, that doesn’t count as outside interference from Superman 
Both Batmen will study each other, and each will come to the conclusion that the other is expecting him to fight just like Batman. So both of them will decide to fight completely unlike Batman would.
What follows is the longest, knock-down, drag-out schoolgirl hissyfits in the history of comicdom. The Batmen will come at each other, shrieking obscenities, flailing wildly with ineffectual blows until one of them takes a scratch across the cheek and falls into a whimpering heap. This one will then realize that since the other one isn’t fighting like Batman, not matching the other one’s fighting style would be an un-Batmanlike thing to do, and thus the wounded one can begin to use all his fighting skills and the other one wouldn’t expect him to.
The scratched Batman will proceed wipe the floor with schoolyard Batman until Schoolyard realizes that he can’t win this way. He will then try to use all his fighting skills to catch up, but it’ll be too late - one Batman has only a scratch, while the other has a variety of bruises, broken bones, and contusions.
So the winner is the one who gets wounded first.
Wait. Are you contending that Batman is dumb enough to fall for the old “Mesmerizing Yellow Circle” trick? Bah. Batman would see right through that.
So…
Batman has X-Ray vision?
It’d be a never-ending fight. They’d each block each other’s moves so it’ll go nowhere. But, if we start getting picky then I’ll choose the yellow Batman, 'coz the yellowness will distract the non-yellow Batman, and Yellow will eventually take advantage.
;j
Okay, here’s how it would fall out.
Yellow Circle Batman and No Yellow Circle Batman will first get into a preliminary battle within the first few pages of the comic book. In this case, they will happen across each other when they use their Bat-radios to call for their respective Batmobiles, thus alerting each to the presence of the other. They will engage in a mighty battle for a few pages, during which each one of them is badly injured. Both Yellow Circle Batman and No Yellow Circle Batman will crawl back in a trail of his own blood back to his respective Batcave, each to lick his wounds. While he recuperates, each Batman will analyze the fighting style of the other, and run analysis on each Batcomputer.
It will become evident to each Batman that he is fighting someone who may be a clever duplicate of himself, or someone at least sufficiently coached in impersonation, and from this will conclude there is a nefarious plot. Yellow Circle Batman will think No Yellow Circle is out to kill him and take over Gotham City; No Yellow Circle will reach the same conclusion.
In order to determine who is behind this nefarious plot, each Batman will try to find out who is behind it all, and capture the other Batman in order to interrogate him. This is accomplished by having each Batman set a trap the other cannot possibly resist: an ad in the newspaper, offering a sizeable sum for an actor who can impersonate Batman! (This cannot fail; it worked on Sherlock Holmes in the pastiche “The Unique Holmes,” after all, and we all know Bats is a big fan of the Great Detective.)
Each Batman will then take the other prisoner, and with both of them Bat-a-ranged to identical steel chairs, they will proceed to beat the crap out of each other in order to determine who the other is working for. They will bounce around, tied to chairs, assaulting one another, until each Batman crawls away from the fight in the nick of time.
At the end of the issue, each Batman will hit upon the clever idea of infiltrating the other Batman’s base of operations. No Yellow Circle will paint his circle yellow; Yellow Circle will paint his black. Each Batman will then cleverly stroll into the other’s Batcave and defeat all the security devices therein, search the Batcomputer of his rival, and discover that the other Batman is now, at this moment, infiltrating his Batcave!
Each Batman will then hit the Bat-self-destruct switch and blow up his Batcave, killing the other Batman.
FISH
This is so simple as to be tautological. Which Batman wins? The real Batman beats the duplicate. But how do we know which one is real? Elementary: You pit them in a fight against each other, and the one who wins is the real one. How do we know this? Because the real Batman beats the duplicate.
I mean, really, it’s obvious!