Going with Goku.
I know a lot about both characters.
Goku is CONSTANTLY training and improving himself throughout the anime. He's a master of multiple martial arts trained by various teachers, supernatural beings and champions (Grandpa Gohan, Roshi, Different Kais, etc.). Goku has achieved the Super Saiyan forms that make him quicker and stronger. Let's not forget he is also capable of firing energy blasts that have completely dissolved enemies.
Superman is more of a brawler, he has been trained some by Batman, Mongul II and is reported to be a boxer, but essentially he's displayed punching people and rarely showing any technical prowess. He has been seen "hyper powered" when closer to the sun and does rage out on occasion. His heat vision has been shown incinerating foes but he rarely uses it to hurt human enemies.
Overall Goku wins. If you want to break it down, I can see a Pre-Crisis Superman probably pushing Goku to Super Saiyan 2 or 3. However the Post-Crisis/New 52 Supes I don't think could beat a Super Saiyan 1 Goku.
The only chance I see Modern/New 52 Superman beating Goku is perhaps fighting a pre-Namek saga Goku. Especially around the time when Raditz killed Goku.
The difference is Goku might hold back some because he likes to test himself. Like Superman, he's his most dangerous when those he cares about are in danger and he's fighting to protect others.
You throw Vegeta in there and you'd see him ruthlessly dismantle Supes.