Bauckham essentially makes the case that Mark was indeed the translator and transcriber of the eyewitness Peter, and that the gospel of John was indeed authored by the disciple John. I'm unclear on why people might think these arguments are in any sense novel, but then I've not yet read the book.
Crossley puts up a weak defense of the cricitcal scholarly consensus regarding these sources, which is essentially that they were associated with particular names of disciples long after they had been in circulation and use within the churches. He fails, for example, to press the question of how Peter could have forgotten the amazingly high Christology of Jesus himself along with several amazing miracles when recounting the his eyewitness tale to John Mark. This discussion could certainly have used a detailed drill down on the differences between John and Peter's allegedly eyewitness stories.
Overall, Bauckham talks so much and Crossley fails so hard in his role as challenger of Bauckham's approach that the radio host has to step in to ask harder questions. These eps are essentially useless as debate.