Nye did not win, because he was fighting the wrong war.
Nye argued like a scientist. He presented the evidence, gave logical explanations, and generally relied on demonstrable facts. He did a flawless job, but changed absolutely no-one's mind, because anyone who cares about science, reason and evidence already accepts evolution.
Ham didn't even really argue. He just riled people up for a crusade - it was the evil liberal commie atheists trying to teach satan's lies, and him and his book of JESUS that showed the big bad man up. He also did not convince anybody, but he can count it as a win because he got people who believed in the general idea of creationism to believe specifically in his branch of creationism.
I've said it before, and I'll say it again: when you argue about creationism, you are not arguing science. You're arguing theology. If it were me on the stage with Ken Ham, I wouldn't bring slides of radiocarbon dating and fossil evidence, I'd bring quotes from Augustine and Aquinas. I'd point out that some of the earliest work leading to evolution was done by Gregor Mendel, a friar in the Augustinian order. I'd use some choice words from Pope Francis, who, even if you aren't catholic, you have to admit he's probably read the bible at least a few times. I'd present a history of creation that matches both scientific evidence (literally) and scripture (figuratively). And then I'd attack his own character, not with the insults of the scientist, but with the insults of a religious man. I'd ask rhetorically how he thinks he can interpret scripture for the rest of us. I'd make him out to be a fraud and a cheat, hijacking religion for his own gain (which, to be fair, he kind of is).
That's how you argue with a crazy person - with more crazy. He, and his followers, don't give a single fuck about the truth. So take them down within their own framework, not from your own.