Both Superman and Batman are my favorite characters in DC, and I've read a lot of their books, graphic novels and currently, I'm enjoying their respective All-Stars book.
And from what I've read and concluded between these two great heroes as far as this thread is concerned, is the writers. There have been far too many writers who generated a lot of great stories about Batman defeating his enemy with his intellect. And there have been far too many writers who have generated stories of Superman defeating his enemy with brawn. Thusly, this process is imbedded into the world's psyche, Batman is the smartest super hero and Superman is the strongest super hero.
When in truth, Superman is as smart as Batman, and in fact smarter. He's the son of Krypton's most influencial mind. Superman has access to technology far superior to Batman, which in turn leads him to have access to more information than Batman. Superman's genetic make up already puts his mind at a higher level than Batman, its just, so many writers have not tapped into this truth, which leads us all to believe that Batman is smarter than Superman. Superman is a highly advanced alien species, both physically and mentally, their race has been around for thousands of years longer than humans, which means they've had more time to evolve their brains and intellect.
To make my point I'll use Tarzan as the perfect metaphor. Tarzan, a human, arguably the most intelligent species on the planet earth. But as an infant he was left to be raised by wild gorrillas. Thusly, he grew up with gorilla customs, communication and habits/instinct. Yet, he was always a little above the rest of the gorillas because of his evolved brain. Tarzan was able to live as one of the gorillas, but at the same time, he was able to use tools, memory and ingenuity to become the Lord of the Jungle. Then as soon as he makes contact with more humans, his brain jumpstarts further. Parts of his brain which were inactive, became active. Ways of thinking and seeing things which he never did before, he now does with ease. Yet, with this advanced knowledge, technology and resources now available to him, Tarzan still goes back to living with the gorillas, living as one of the inhabitants of the jungle.
And this is Superman on earth, he is Tarzan and the earth/solar system is his jungle, so no matter how smart the most intelligent human is on earth, Superman is still far more superior. Now I bring this up because, in a fair fight, Batman will prepare for a battle with Superman....this takes time. Which means, Superman will not waste this time waiting, he, too, will prepare for his upcoming battle with the Batman.
Superman knows more than anyone how smart and resourseful Batman is, so he will not engage him without being fully prepared. In truth, both Superman and Batman are heavily aware of each of their strengths and weaknesses, each of them know how to expoit and counter each other's moves. But in the end, Superman can outlast Batman, no matter how prepared Batman can get. The facts are, The Batman needs kyptonite, magic, technology, food, water and rest to take on Superman on an all out battle, while Superman only needs the sun and a lead-impregnated suit to do battle. Batman may find away to block out the sun around Superman, but the last son of krypton is a living battery, so even if the sun is covered up, Superman can go a few days, maybe a week without the sun and still be able to lift Mt. Fuji.
Superman can easily, as a brutal resort, dive underground, then he can lift the entire town/county/state that Batman is staying/preparing for the fight, and take it to outer space. Then Superman can drop the entire mass of earth on the surface of Mercury which is facing the sun, then attack from a distance.
Batman has no chance, should Superman resort to this means of combat.