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The key "difference" that I've seen is that Libraries are expensive in terms of gold in wages, while the church costs more in raw materials to build and space inside the city. You are right that the cathedral does not boost churches.
Some further testing on the tithe front has revealed that paying more than 1000 gold to each structure has done "nothing" so I've shifted focus a bit- maybe it's mechanics are more closely tied to the witch as a counterbalance of sorts? I've yet to test this, but I mean to on my next day off.
Somewhat off topic, but I don't usually build the cathedral in my cities. It's bonus of "converting" vikings is way more trouble than it's worth, as the converted vikings are hauled away by their peers, and I'm suddenly short housing for all the newcomers that do make it inside, which dings my overall city happiness considerably.