I don't know if you're old enough to remember it, but PBS did run, during the 1970s and 1980s, a program called "The Firing Line," that was supposed to be a debate on different ideas. It was hosted (if memory serves) by the now deceased William Buckley, a noted conservative commentator for that time. As noted, that program eventually turned into a screaming match between the right and left.
On the other hand, several public radio stations (including KJZZ in my current hometown of Phoenix) have been carrying a traditional style debate program (again, if memory serves) called "The Great Debates." As I understand it, the show is taped in front of a live audience on the East Coast, and, unlike "The Firing Line,", the moderator does his best not to reveal which side he is on with regard to the subjects being debated. I believe the network sponsoring the show is American Public Media (APM), and I've heard the program for over a decade now without the debates becoming a screamfest.