Round one, could go either way, but I'd bet on Solo winning, or more out of 10.
Round two, Kirk demolishes. This is the guy who took on Khan, wrestled a Gorn, punches Nazis and Cowboys and Gangsters, oh my! Takes on Klingons. Got shanked in the kidney by an Orion disguised as an Andoran and still managed to take the fool out with the flying-ass-attack. Nearly matched a sex-crazed Spock while being handicapped due to Vulcan's atmosphere. Augments like Khan are x5 human strength, Vulcan's are x3, Klingons are x2 and the Gorn, they're strong enough to casually toss 1ton boulders.
Young han survived a beating from a wookie was able to casually rip a man's arms off. He seemed to be a pretty decent shot on the mining planet and could hold his own against a (force sensitive?) Mob boss with a laser knife. I vote young han.
He didn’t do anything impressive. Chewie was going to drown him and he made a deal. Kirk would beat the shit out of him. He was saved by Q’ra. Kirk is just flat out superior to Han.
I still feel that he was more impressive against chewie than Kirk was against khan (assuming Chris pines version). He was also quicker on the draw than Becket on their last encounter, and Becket' s marksmanship was a lot more impressive than kirk's
Khan is a much better fighter than Chewie who is just strong. He isn’t skilled at all in hand to hand fighting. He caught him by surprise. Beckett was far better with a weapon.