I am not familiar with Ben Shapiro and his magazine, Truth Revolt, is associated with David Horowitz's Front Page Magazine and therefore I can safely say that he represents criticism from a Jewish right-wing conservative perspective.
Beinart we are, of course, familiar with from his time with Marty Peretz at the New Republic and his relatively recent incarnation as a progressive-left Zionist. People tend to forget that Beinart's views were not quite so "progressive" when he supported the Iraq war in 2003 under the Bush II administration.
In any case, it is an interesting exchange that turns sharp toward the end.
I think that you should give it a listen and endeavor to be fair to both gentlemen, even if they are less than fair with one another.
And, in the interest of fairness, it should be noted that Shapiro did, in fact, call for the ethnic cleansing of Arabs from all of Israel in a 2003 piece entitled, Transfer is not a dirty word.