As I understand it, they're fans of each other's work. There was another show where the two of them and someone connected to Idoling! all sat down to talk over lunch. I believe it was said that Akimoto thought Tsunku had an inner middle school girl, to which Tsunku replied that Akimoto had an inner high school girl. (Or something to that effect.) I think this was in regard to their ability to write lyrics that girls can relate to.
I do know that Tsunku was a big idol fan back in the day, and was particularly a fan of Onyanko Club. I can remember him stating somewhere that he felt AKB and H!P were like Toyota and Nissan. At the very least, there's some mutual respect there. I mean after all, who else can really relate to what they do except each other?