I did a run with Byzantium using WOTP to see what my experiences were. I wanted to see just how much I could squeeze out of the belief.
From turns 114 - 127 I converted France who was my only neighbor. France had no religion, but even so I managed to get 600 culture from the effort. Its less than I would get from AP, especially considering my own city conversions....but it was better than I expected.
But then the real test took place a bit later. I went ahead and used some faith to get my GP for enhancing, and to buy Monasteries.
Then starting on Turn 192 I bought a massive amount of missionaries (54 in total!!!!) before the Renaissance cost increase (with Borobodur). I also have Fealty for a further cost decrease, making my missionaries only 120 faith at the moment.
I found my target.... Babylon with a holy city, and then Denmark to the east of that....who had been taking the pressure from Babylons religion. So I went in for the kill!
Now for this test, I decided not to abuse any missionary attrition. I wanted to see how good this was straight up, so I had Open Borders on. That said, Babylon's holy city was only taking 500 pressure at a time.... which was very strange because I didn't see any holy buildings for the beliefs. The other cities took 900 pressure at a time. I generally bombed them until the culture dropped to 90, then I moved on to another city. I converted all of Babylon, a bit of Denmark, and a couple of CS. Ultimately I wasn't trying to be super optimal, just converting the cities I found along the way.
After the dust settled by Turn 200, here are the stats:
Culture Gained: 20,477
Faith Spent: 6,560
Culture Per Faith: 3.17
Culture Per Faith (removing Byzantium's 15% discount): 2.71
Missionary Charges: 141 (Avg: 2.61 charges per missionary....aka some missionaries were before borobadur, and I used a few charges to finish my own city conversions).
Avg Culture Per Charge Spent: 145 (this is probably the best metric because this ignores the faith spends that have a Byzantium bias and just shows us raw missionary efficiency. Aka for any civ, even one with lower faith....could expect this kind of efficiency)
Culture Conclusions: So I already knew that WOTP scaled well into the late game....but what this run showed me was just how good WOTP can be in the midgame. These are very good numbers, 145 culture per charge is honestly as good as AP is in the initial expansion phase, and this belief maintains it a lot longer. While it does take longer for this to ramp up compared to AP....it holds its strengths for much much longer. Further, in this run I was mostly isolated, and my neighbor did not have their own religion. Had I been more religiously crowded, I could have gotten those culture numbers even sooner.
Overall I was incredibly impressed with WOTP culture output, and I now agree with the other posters in this thread that it blows AP away in terms of culture output.
So I've often said that tourism in the early game does so little I basically ignore it as a yield. However, WOTP provides such a powerful and focused tourism benefit that it actually needs to be accounted for. I produced ~17,500 tourism to Babylon along the way (rough number, I didn't track it precisely but I have ~20k right now and other civs I haven't bombed are about 1500). That is enough to be influential for days...which this early in the game does mean something from a trade route perspective. The fealty finisher actually works really well here. I had the 10% open borders bonus, but then once I hit the tipping point and made Babylon my religion, I was now getting a 50% tourism boost from shared religion. That combined with the bombs gave me an exceptional tourism push.