Surfer has too many options for dealing with Superman. Whether is the popular energy drain or kryptonite knuckles theories stated in earlier posts or something more exotic like zapping him with blue kryptonite radiation. Superman is pretty straight forward in his fighting. All he can really do is punch, kick, use heat vision or cold breath. Surfer is immune to temperature extremes so excesses of heat and cold will not work. In terms of speed they are pretty equal so a blitz attack is out for both of them. Superman is no more likely to beat Surfer unconscious than Surfer is to do the same to Superman there would have to be an extra that one has over the other and the Power cosmic gives Surfer that edge.
With the "losers Earth is destroyed" edit added by this threads creator the scales tip in Surfers favor even farther. As we saw when Superman was being mercilessly tortured by Gog, we learned he would under no circumstances kill an opponent no matter how many lives were saved. Surfer would have no problem with killing Superman if it meant that his Earth would be spared. Superman is a hero that sees everything in black and white whereas Surfer is a hero that has a more shades of gray perspective.