If they fought and they knew they were both good guys and stuff. Supes would fly fast and true and start punching and kicking or use heat vision.
Surfer IMO would be dodging and blocking and maybe get banged up a bit. Sufer would blast away at supes and supes taking damage. After a while. Supes would just continue to use the same tactics but maybe just fighting smarter to end it quicker without killing him, basically punch harder in this case. Surfer would fight smarter and change tactic all together. That is when SS would scan his fellow hero for any weaknesses to exploit. he will find them and then just do what was inevitable in every superman vs match up in KMC.