All from a deity perspective, haven't played on lower difficulty in over a year so can't really comment on it, but it definitely changes the values a lot.
Piety
7 - Opener: If you go for religion and you're not a religion generating Civ, this is almost required. Not only is it excellent when going wide, but it's needed for a good pantheon, shaving 4 turns off in the earliest stages of the game.
7 - Organized Religion: This is an absolutely necessary follow up to the opener if you are still on the religion plan, as it pretty much doubles your faith output.
8 - Mandata of Heaven: Although a bit situational, this allows you to spread your religion earlier and cascade into religion buildings faster.
4 - Theocracy: 10% base gold output is pretty bad, especially in BNW. You'll rarely get more than 2 gold out of it per city. That puts it a bit behind most other gold generating policies.
2 - Religious tolerance: The usefulness depends greatly on circumstances, but in general a minor amount of culture or faith is not worth a policy.
6 - Reformation: Reformation beliefs are in general too weak to spend a policy on, even if you go all in on the religion.
6 - Finisher: The extra culture may be good but getting the settled Prophets to work has never really been useful for me.
Patronage
8 - Opener: The Forbidden Palace is an almost impossible dream, even if you beeline banking and have an Engineer ready. However, the slowing of the influence decay alone is enough value on its own.
6 - Philanthropy: Still as good as before. The ideology generators are better, but they come late.
6 - Consulates: Pledges + Consulates is great, but also situational.
7 - Scholasticism: For a tall empire, it's very powerful if you manage to ally a lot of CS. Value diminishes a lot as you expand.
7 - Cultural Diplomacy: Can be extremely valuable if things are tight. In BNW, I feel the only resource you really need is Oil, but you need a LOT of that, and this can provide just that.
1 - Merchant Confederacy: Even under the best circumstances, this isn't going to get you more than what, 8 gold ? Extremely weak.
5 - Finisher: The fact that you have no control over what you get, combined with the low frequency, means that this isn't really worth much. If you are Sweden, then this cascades nicely. If you're not, it depends on luck a lot.
Aesthetics
5 - Opener: Uffizi is too popular with the AI to get frequently, and usually not even worth building. Extra great people is good but only if you go cultural. I never needed more than I could build normally to defend myself. This makes their application very pigeonholed.
7 - Cultural Centers: This one is actually pretty good in general, as extra production is always a good thing.
4 - Fine Arts: The amount you get from this is very limited, even in good circumstances it'll be less than the culture you get from even one city state.
7 - Artistic Genius: An extra artist is good, but the fact that you can choose exactly when to get this makes it even better, since that makes getting all theming bonuses that much easier.
8 - Flourishing of the Arts: The boost is massive, and if you are going culture and have no wonders at all, you are in a lot of trouble anyway. Just need one wonder per city. The golden age also gives you everything you could possibly want, as you will probably just want to chain them together in your culture games.
7 - Ethics: This pays itself back and more if taken early enough, making this an essentially 5 policy tree rather than 6.
9 - Finisher: Double theming bonuses are nice and all that, but the real sweetness is quite obviously faith buying 3+ Great Musicians after you have the Internet. Again, like all other policies in this tree, it's all limited to Cultural games.
Piety
7 - Opener: If you go for religion and you're not a religion generating Civ, this is almost required. Not only is it excellent when going wide, but it's needed for a good pantheon, shaving 4 turns off in the earliest stages of the game.
7 - Organized Religion: This is an absolutely necessary follow up to the opener if you are still on the religion plan, as it pretty much doubles your faith output.
8 - Mandata of Heaven: Although a bit situational, this allows you to spread your religion earlier and cascade into religion buildings faster.
4 - Theocracy: 10% base gold output is pretty bad, especially in BNW. You'll rarely get more than 2 gold out of it per city. That puts it a bit behind most other gold generating policies.
2 - Religious tolerance: The usefulness depends greatly on circumstances, but in general a minor amount of culture or faith is not worth a policy.
6 - Reformation: Reformation beliefs are in general too weak to spend a policy on, even if you go all in on the religion.
6 - Finisher: The extra culture may be good but getting the settled Prophets to work has never really been useful for me.
Patronage
8 - Opener: The Forbidden Palace is an almost impossible dream, even if you beeline banking and have an Engineer ready. However, the slowing of the influence decay alone is enough value on its own.
6 - Philanthropy: Still as good as before. The ideology generators are better, but they come late.
6 - Consulates: Pledges + Consulates is great, but also situational.
7 - Scholasticism: For a tall empire, it's very powerful if you manage to ally a lot of CS. Value diminishes a lot as you expand.
7 - Cultural Diplomacy: Can be extremely valuable if things are tight. In BNW, I feel the only resource you really need is Oil, but you need a LOT of that, and this can provide just that.
1 - Merchant Confederacy: Even under the best circumstances, this isn't going to get you more than what, 8 gold ? Extremely weak.
5 - Finisher: The fact that you have no control over what you get, combined with the low frequency, means that this isn't really worth much. If you are Sweden, then this cascades nicely. If you're not, it depends on luck a lot.
Aesthetics
5 - Opener: Uffizi is too popular with the AI to get frequently, and usually not even worth building. Extra great people is good but only if you go cultural. I never needed more than I could build normally to defend myself. This makes their application very pigeonholed.
7 - Cultural Centers: This one is actually pretty good in general, as extra production is always a good thing.
4 - Fine Arts: The amount you get from this is very limited, even in good circumstances it'll be less than the culture you get from even one city state.
7 - Artistic Genius: An extra artist is good, but the fact that you can choose exactly when to get this makes it even better, since that makes getting all theming bonuses that much easier.
8 - Flourishing of the Arts: The boost is massive, and if you are going culture and have no wonders at all, you are in a lot of trouble anyway. Just need one wonder per city. The golden age also gives you everything you could possibly want, as you will probably just want to chain them together in your culture games.
7 - Ethics: This pays itself back and more if taken early enough, making this an essentially 5 policy tree rather than 6.
9 - Finisher: Double theming bonuses are nice and all that, but the real sweetness is quite obviously faith buying 3+ Great Musicians after you have the Internet. Again, like all other policies in this tree, it's all limited to Cultural games.