I'm not a big fan of either, but if I have to pick one, it has to be Batman. Of all of the Batman stories I've read, I like the late Bronze Age, just before Crisis ones the best. The Detective stories from the early Bronze Age, with their supernatural bent, are pretty bad, and I don't dig Silver Age DC in any way, shape, or form (at least not for their main heroes; just too darn silly). Current ones have him at god-level abilities; he's perfect at everything and always five steps ahead of everyone else, so threats like the Council of Owls seem ridiculous, as he would have HAD to have known about them or else he's an idiot.

Superman has never appealed to me at all. He's too OP and attempts to make him vulnerable come off as forced or hokey.

Two for Superman then.

Yeah, I feel like Batman has better tangential media from the comics.

I'll go with Batman.  Though Superman has Jerry Siegel, Joe Shuster, Curt Swan, George Reeves, Christopher Reeve, those fantastic Silver Age tales, that squinty-eyed, Champion of the Oppressed early period, the Fleischer cartoons, and an element of tragedy which added a level of depth you almost never saw from DC's major characters (even Edmond Hamilton and Eliot Maggin's Luthor seemed real); he also didn't have much going for him during the Bronze Age (with occasional masterpieces such as "The Return of Jonathan Kent" and "When you wish upon a Planetoid" aside); turned Lois Lane into every chauvinist's ideal woman (yes, during the same Silver Age period I adore so much); doesn't have as great a Rogue's Gallery as he should (though it's better than he's often given credit for); and he hasn't been seen or heard from since Crisis.

Batman?  Despite lousy Bob Kane artwork ruining much of the early 1940's, a rather unimpressive update in 1964 (costume and Infantino artwork aside), whatever David Reed was doing in the 1970's, too much Frank Miller influence, and probably the worst villain in comics since Alan Moore got his hands on him; he's also got Bill Finger, the best Rogues in comics, Dick Sprang, Adam West, Jim Aparo, all the qualities a superhero needs to thrive (He's a Detective-Scientist-Escape Artist-Creature of the Night who's as at home in the shadows as he is fighting aliens in broad daylight where he leaves a bat-shaped shadow even when he's dressed as Bruce Wayne), the coolest hideout and car collection there is, and the greatest villain in comics until A Killing Joke came around.  Even after the Crisis he got that wonderful Grant/Breyfogle run and the animated series.

Batman...he's darker and has a better choice of villains.

Great to see so much Bat love still around in spite of the BatGod BS which has ruined the character. Give me the human and fallible guy who has friends and family grounding him realistically so that when he fails he overcomes the failure to achieve something better and there is a difference to being prepared for many eventualities and having a plan for taking out your partners and friends. Bruce Wayne is damaged emotional goods, not psychotic mental patient who has become as horrible as the villains he combats.

And Batflunkie, you can rest assured there are other lovers of Steel. I bought all of his series in the day and adore John Henry Irons even if DC has somewhat misused and seems to forget his importance these days.