Each of these methods contributes useful priors for "regular" one-parameter problems, and each prior can handle some challenging statistical models (with "irregularity" or several parameters). Each of these methods has been useful in Bayesian practice. Indeed, methods for constructing "objective" (alternatively, "default" or "ignorance") priors have been developed by avowed subjective (or "personal") Bayesians like James Berger ( Duke University ) and José-Miguel Bernardo ( Universitat de València ), simply because such priors are needed for Bayesian practice, particularly in science.  The quest for "the universal method for constructing priors" continues to attract statistical theorists. 
If you liked An Intuitive Explanation of Bayesian Reasoning , you may also wish to read A Technical Explanation of Technical Explanation by the same author, which goes into greater detail on the application of Bayescraft to human rationality and the philosophy of science. You may also enjoy the Twelve Virtues of Rationality and The Simple Truth . Other authors: E. T. Jaynes: Probability Theory With Applications in Science and Engineering (full text online). Theory and applications for Bayes' Theorem and Bayesian reasoning. See also Jaynes's magnum opus, Probability Theory: The Logic of Science .