[tel]

I'd also like to point out that there's a huge policy impact of one method over the other. Since Frequentist and Bayesian methods disagree in how we should construct and evaluate models then almost of all scientific practice is impacted. In practice it seems that good science can arise from either method, but duality here leads to a great deal of policy confusion since things that are taken as holy by many scientific practitioners are given to questioning when you introduce a complementary method.

[mattkrause]

You can also think about this in terms of guarantees. Frequentist methods can give you confidence about the long-run performance of a method, by controlling the familywise error or false discovery rate. In other words, this procedure will only be wrong $\alpha$ percent of the time. Bayesian methods don't really give you that, but they may give you a more coherent summary of the state of the world right now.