Round two of the Bill O'Reilly and Jon Stewart face off went to Jon Stewart.

Simple as that folks. O'Reilly came out playing rope a dope, saying he was thinking of making Stewart his VP pick for a fictional presidential ticket and wanted to vet him.
Clever move but Stewart was more than able to outfox the old pro.
On almost every issue they went over Stewart won the argument, even getting O'Reilly to admit he apologized on air when no weapons of mass destruction were found in Iraq.
On Iran, Stewart really landed some uppercuts. He pointed out that Pakistan and other countries had nuclear weapons and making Iran an obsessive focus was never going to stop the spread of them.
He even got a great dig in at O'Reilly's war on Christmas by declaring a war on Hannukah.
On global warming he seemed less sure and O'Reilly won that round.
The funniest line was when Stewart told O'Reilly he would not want to be his VP because the only job he'd get would be lighting the White House menorah, a remark that even brought laughter from the studio workers.
On the final question of Sarah Palin, Stewart held his own,denying he didn't like her personally , saying simply he didn't know her.

He knew he was protecting an easy points lead at that point.
So night one to O'Reilly, night two to Stewart, a draw overall.
Lets do it again folks, it makes for great television.