Well, that is an exaggeration, but they were both in the same room at points and are friendly. I have just returned from Computing in Economics and Finance, 15th conference of the Society for Computational Economics, held at the University of Technology in Sydney, Australia this past week. While dominated by wonkish quants who worship DSGE models in central bank basements ("putting some learning in them will make everything all right"), there were also some heterodox types, most prominently Australia's Dr. Doom, aka, Steve Keen, a Post Keynesian who has been math modeling Minsky since before it was fashionable and is now all over Aussie media having loudly called the crash early. He also runs a lively blog, Debtwatch. Brenda Rosser and I saw him perform, which he does well, with his array of slides of misery and mounting debt, and so on.
Dr. Bounceback is Jim Morley of Washington University in St. Louis, whose talk was not as well attended as Keen's, but interesting nevertheless. He has recently been touted on some blogs (econbrowser at least) for being out on a limb as the most optimistic forecaster around, arguing that the depth of the fall will in the pattern of inventory adjustment models give us a strong bounceback, and while he was a bit more cautious in his talk, bringing in model averaging and recognizing that the current situation has other factors messing things up, he is still probably the strongest voice for a "V" pattern, as opposed to a "W" or a "U" or an "L," as these things get labeled in the world of alphabet business cycles. One can access a description of the bounceback model in a paper by Morley and Jeremy Piger, "Practical Computation of the 'Model-Free' Business Cycle"(pdf). I note that while some may think he is very conventional, he is not that big a fan of the DSGE models, and is friendly with his Post Keynesian colleague at Washington University, Steven Fazzari.