Superman wouldn't necessarily be able to find Batman. I still say Batman's chances depend on his ability to deny Supes the direct confrontation.
Superman is "faster than a speeding bullet." (double-digit Mach numbers...)
Superman can see through anything but lead.
Superman can see tiny objects from miles away.
Superman can see microscopic objects with his naked eyes.
Superman's hearing is so good he can pick individual heartbeats out of crowds.
Superman can fly.
Superman is strong enough to dead-lift thousands of tons (rocks in a fault (the movie), Luthor's yacht (Man of Steel))
Given these abilities the amount of ground he could cover in a search is potentially staggering, so Bats really only has two options for trying to stay hidden:
!. Never stand still in any edifice that isn't completely lined with lead. (Which would actually give supes more info than bats would prefer...)
2. Leave the planet. Even Superman can't get him in space without a space ship.
See eventually, no matter how much hide and seek bats wants to play, if there's a direct confrontation to be had, Superman will have it. And he will win.
Nobody prefers powerless heroes because it's chic or fashionable.
I disagree. Everybody on this board (including me) likes to be intellectual about this thing or the other, and in this case the idea of backing the powerless hero is an intellectual favorite, because it's romantic. The guy with no powers is supposed to get trounced, but he can prepare, and he can be determined and he can beat the odds, yadda and yadda. Right.
But every now and then I like to be an objectivist, and in an objective universe, if two guys want to kill each other and one has no powers and one has Superman's powers the guy with Supe's powers will eventually win. The other guy can't hide forever, no trap will stop the powered guy completely, and using his one weakness against him only works if he doesn't have a countermeasure for the weakness.
I just find heroes who are invulnerable with single exceptions and can otherwise just power through fights with brute force incredibly dull. Just like rooting for Lebron James is boring if his opponent is a ten year old girl.
If the ten year old girl is wearing the jersey of a division or conference rival, I'm sure there are plenty of Cavs fans who would scream themselves hoarse rooting for King James to send her home crying.
The trick to not making Superman boring is finding villains he can't beat with brute force alone (or at least with one shot). You put him up against Mr. Mxyzptlk or Doomsday or Darkseid and watch what happens.