I have to go Gambit on this one. I think we can all agree that Gambit is faster (bullet time), more agile, and a better hand to hand fighter. I think their physical strength is pretty similar but if it comes down to it, Gambit would win in fisticuffs.
This battle is going to come down to powers though. Cyclops has the edge in brute force and does well against durable non-evasive opponents (Sentinels, Hulk, Juggernaut) but I don't think he performs as well against agile dodgers. He nailed Nightcrawler but he knew where he would appear and the blast was waiting for NC as soon as he did re-appear so evasion was not an option.
Gambit can and would dodge optic blasts unless they were point blank. Cyclops is not evasive. He would be reliant on shooting down the projectiles for defense. I think Cyclops would have to take his attention of Gambit allowing the thief to get the advantage.
I see them both unleashing their powers at the start, and I would go as far as to say Cyclops could/would blast Gambits cards while in mid-flight.This is where Gambit would take the advantage though. The dust and confusion from unleashing such powers benefits Gambit and his elusiveness. I think once Cyclops loses sight (heh) of his opponent, he would have a hard time relocating him. Time delayed charged objects, attacking from the shadows, and we can't overlook the potency of a fully charged deck of cards (I'm looking at you Gladiator) lets Gambit edge out a victory.
Cyclops is the better leader and strategist, but in a RANDOM encounter in a SOLO battle in a downtown setting at NIGHT all favors Gambit.