I just finished Book of the New Sun and thought I'd start this series. So far the two have no relation (besides perhaps taking place in a shared future). Immediately, I noticed that the beautiful writing style of the New Sun series had been replaced by a third-person, straight-forward narrating style... but it grew on me. The themes are deeper than the plot, and in the end it reminded me of Breaking Bad set in the future, for a Catholic audience. It's better than I'm describing.
Macmillan did a great job editing the Kindle version. Generally speaking, their Gene Wolfe books are unforgivably sloppy on Kindle, but I didn't encounter any careless mistakes here. Buy it!