This one's too close to call, IMO. It could go either way in a heartbeat.
It's unlikely the Surfer would automatically know of Superman's weakness to red sun radiation or kryptonite, so that rules out those options of attack. Nor could he turn Supes into Krypto... his manipulation powers are usually restricted to restructuring inorganic matter - probably because the Surfer tries not to kill people (this attack on an opponent would be fatal). There are some limitations to the Surfer's powers - he's not omnipotent. Also, the power cosmic is not magical in origin, so Superman has no vulnerability there.
Basically, the power cosmic is like a big store of universal energy the Surfer can tap into to augment his powers and abilities. It typically enables him to have the approximate strength of an enraged Hulk (yes, it's true), and throw around vast amounts of destructive energy.
Superman is capable of beating even a cosmically-powered Surfer, IMO. He probably WOULD beat the Surfer without his power cosmic in effect, as Supes physically outclasses him without it. With full access to his cosmic power reserve, the Surfer is able give Superman all he can handle. He would probably be the most powerful opponent the Man of Steel has ever faced. Superman has the resilience to take most of what the Surfer can throw at him, but the Surfer can take everything Supes can dish out, too.
It could come down to who lasts the longest. Superman has an enormous, but finite level of endurance and energy. The Surfer's power source is practically unlimited. That could tell the tale, though I can still see the scales tipping in Superman's favor - maybe as much as half of the time.