AFAIK, the breakdown is this:<p>Frequentist is a special case of Bayesian. The Frequentists have much more mature tools, because they've been working on them since Gauss's day. Bayesians (especially less experienced ones) may claim that that Frequentists are old school, outdated, and don't teach undergrads the new Bayesian way of doing things.<p>Bayesian methods are more flexible and general, but are often slow (computationally), and can be too flexible. A Bayesian can prove anything. Frequentists have trouble eliminating some biases (because their tools aren't as flexible), but also have trouble purposely (or subconsciously) biasing their results.<p>I'm not going into the specifics of the methods here, just the source of their disagreements.