real.geizterfahr: Seriously, what could Batman do? Hit Superman? Throw some explosive crap? Run him over with his Batmobile? Tickle him? oO It's SUPERMAN! The guy who carries airplanes! The guy who doesn't have a scratch after being burried under a skysraper! What is Batman compared to him?
The whole fun of a Batman/Superman fight is in how mismatched they are, and seeing what Batman comes up with. Unlike most fights that are about being faster or stronger this one is all about being clever and creative. And yes, some outstanding circumstances aside Batman has got to lose. But the fight can still be very creative and fun, much more than when Superman is just punching someone like Doomsday.
My favourite is probably in the New Frontier special issue, with the first meeting of that versions of Batman and Superman, with Supes sent by the goverment to capture Batman. Batman has this whole plan set up, and he beats the crap out of Superman, to the point where Clark is really scared for maybe the first time in his life, and it's pretty much only that desperation that gives him strenght to win, at which point Wonder Woman shows up and break up the fight. A great example of a Batman/Superman duel, that does justice to both characters.
Breja: Technically it only proved that Wayne Enterprises exists. I know that sounds stupid, but there was a mention of Wayne Enterprises on the Flash tv show, and there is very definately no Batman in that universe, so sometimes an easter egg is really just a wink to the audience, nothing more.
RWarehall: I'm not sure I'd say for certain there is no Batman. The shows just focus on a different area. He certainly could be added...
I'm pretty sure it's been made explicit by the creators that Batman (and Superman) are not on the table. Also, I feel Batman would at least have been mentioned by this point in the Arrow/Flash universe. Ra's al Ghul would say something like "you're good, but you're not the Detective", or something like that. I know in theory they might add him at some point, but I feel this universe makes more sense if we assume it's Batman-free.