For me, it was always the book first. White pages, no browning on the edges, looking like it was freshly printed. Most times when you find the book, it then follows it is the Church copy. Sheer volume leads to the Church books being more available, more noticeable, more collectible, and more likely to fetch a high price. Don't get me wrong, the other peds are very nice but the quantity and name recognition of the Church books almost always makes them the copy to go after if you want an immaculate 80-year old book.
I should add that since I was never a big collector of the top 100 GA books, the Church copies were almost always the only high-quality ped available. Some Allentowns, some Pennsylvanias, almost never any SF copies. Church and Crowley were the primary choices of well structurally-preserved books and Crowleys were always a distant also-ran compared to the Churchs. They are just much more common and easy to find in many titles.