For years, even decades now, the question has been asked, who would win in a fight, Anime's very own Legend Son Goku, Super Saiyan Savior, or Detective Comics very own Man of Steel? DBZ Fans have raged about this, as well as DC fans, heck, even Marvel fans have peaked their heads out. Goku has been classified as the man who can break any limits, while Supes has been classified as the man with no limits to begin with. On calculations, stat wise, most would say Superman, and I agree with this, depending on setting.
In space, under the usual yellow sun, Supes would definately win. Because although Goku SSJ3 would put up a good fight, and SSJ4 would be equal to Supes for a time being, the yellow sun increases the power of the man of steel, which in the long run is limitless, and would be too much, even for Goku at full capacity. This is when Supes has home battlefield advantage though.
Lets give it to Goku, and the outcome is tottaly different. Kryptonians get stronger with solar energy, as oppoesed to Saiyans, who's powers are maxified by the moon. Firstly, Superman values life on Earth, and Goku grew up protecting the Earth, so Goku would offer Superman a chance to get away from the Earth, and the loved ones they both have there, and Superman wouldn't hesistate to agree. So Instant Transmission it is. Goku would teleport the two them to planet far away with deserted life, so no one else could feel the impact of their battle, thus farther away from the sun. Out of the sun's range, Superman's powers are average at best, and so are Goku's. But this is still pretty high for the both of them, both aliens from other planets, they never been averaged. Although Superman tried to fit in, Goku settled for being out of the ordinary and weird as most people called it. Goku and Superman would engage in combat.
For a while, Superman would dominate, knocking Goku a round. Goku would then show Superman SSJ1, which maximizes his power 50x. Goku would began dominating Supes, due to the immense shock Supes would be in that he transformed. Then, after Supes recovered, he would began overpowering Goku again. Goku would then show him transformation 2, which doubles the power of SSJ1. Superman would realize that he transformed once more and get smacked around for a bit. He would then recover and began to dominate once more. He would then try to end the battle quickly, as he sees Goku is not taking the fight seriously. Heat vision. Goku would see it, and kamehameha blast it.
It seems for awhile that Superman might when after all, until Goku decides to unveil the Super Saiyan 3 transformation, tottaly taking control of the energy battle at that point. The Kamehameha makes Superman jump back injures him. He is battered, just barely though. He then launches at Goku full power, while Goku simply blocks and evades all his attacks. Goku then kicks him back, far enough to get some distance between the two of them. Goku decides enough is enough, transforms into SSJ4, which increses the power of SSJ3 ten fold. Night fall,, and the moon is out. He then begans dominating Supes, who can't even dodge attacks at this point, as the speed discrepency is too great. Superman tries a last super-charged punch with all his might at Goku, but he catches it, crushes his fist until it bleeds. And then dragon fist Superman straight to the chest. Done!