First, he noted good-naturedly that Jeremy's connection with B'nai Jeshurun had unexpectedly topped his: Kristol's family had celebrated his daughter's nuptials with a pre-wedding "auf-ruf" (the traditional blessing of the Torah for the bridal party) at the shul, but Jeremy experienced his first date at a Sabbath service there with his future wife.
Kristol is not of the far-right in the Republican party. He says that he would like to see a two-state solution, but disagrees with Ben-Ami's dire warning that the lack of progress toward this resolution is a danger to the democratic and Jewish character of Israel. As Krisotl indicated explicitly, the current status quo is fine with him.
Kristol's lack of knowledge and concern for what's going on was shocking; he admitted to knowing less about the issues than his opponent yet refused Jeremy's invitation to join him in visiting the places where aggressive settlement activity is undermining a two-state solution at an alarming rate. I wasn't close enough to see the self-satisfied smirk almost always planted on Kristol's face that I've come to know from his way-too-many television appearances, where he is a constant partisan advocate for the Republican Party.
These exchanges are featured in the first of three YouTube videos being placed online by J St.:
They went on to joust on what Jeremy regards as intimidation tactics over Congress, exercised by the Emergency Committee on Israel that Kristol helped put together. Jeremy contends that the ECI defames members of Congress as "anti-Israel" for recommending policy measures intended to promote a two-state solution or a peaceful resolution of the confrontation with Iran.
A news article in Haaretz pithily summed up their differences in this passage:
Kristol rejected Ben-Ami’s call for the U.S. president to “lay down the parameters” of a peace deal – 1967 borders with modifications, Jerusalem as the capital of both Israel and the Palestinians, no right of return and a demilitarized Palestinian state. Kristol said that it was not the business of America to “impose” a peace deal on Israel and the Palestinians....
Nonetheless, Kristol surprised many in the audience by voicing clear support for a Palestinian state, saying, “I would be very happy if there was a Palestinian state”. He rejected Ben-Ami’s predictions of a one-state future in which the Palestinians would demand the principle of “one man one vote," saying that Israel has ruled the occupied territories for over 45 years and that the indefinite maintenance of the current status quo “is also an option."