A quick response to the bulleted content:
1) Power / Type 1 error in a Bayesian analysis vs. a frequentist analysis
Asking about Type 1 and power (i.e. one minus the probability of Type 2 error) implies that you can put your inference problem into a repeated sampling framework. Can you? If you can't then there isn't much choice but to move away from frequentist inference tools. If you can, and if the behavior of your estimator over many such samples is of relevance, and if you are not particularly interested in making probability statements about particular events, then I there's no strong reason to move.
The argument here is not that such situations never arise - certainly they do - but that they typically don't arise in the fields where the methods are applied.
2) The trade-off in complexity of the analysis (Bayesian seems more complicated) vs. the benefits gained.
It is important to ask where the complexity goes. In frequentist procedures the implementation may be very simple, e.g. minimize the sum of squares, but the principles may be arbitrarily complex, typically revolving around which estimator(s) to choose, how to find the right test(s), what to think when they disagree. For an example. see the still lively discussion, picked up in this forum, of different confidence intervals for a proportion!
In Bayesian procedures the implementation can be arbitrarily complex even in models that look like they 'ought' to be simple, usually because of difficult integrals but the principles are extremely simple. It rather depends where you'd like the messiness to be.
3) Traditional statistical analyses are straightforward, with well-established guidelines for drawing conclusions.
Personally I can no longer remember, but certainly my students never found these straightforward, mostly due to the principle proliferation described above. But the question is not really whether a procedure is straightforward, but whether is closer to being right given the structure of the problem.
Finally, I strongly disagree that there are "well-established guidelines for drawing conclusions" in either paradigm. And I think that's a good thing. Sure, "find p<.05" is a clear guideline, but for what model, with what corrections, etc.? And what do I do when my tests disagree? Scientific or engineering judgement is needed here, as it is elsewhere.