Thanks for the replies guys. Killbray, if you had an established religion and during the course of the game found yourself expanding next to an AI where the religion of yourself and the AI was fairly equal pressure wise, some of each in close cities, would you use faith for missionaries, inquisitors or wait for a Great Prophet?
Depends. You should look at the cost of the prophet and the age you are in.
Missionaries' and inquisitors' costs increase whenever you reach a new era
Prophet's costs increase the more you spent faith to buy prophets.
This means that you can potentially find yourself in the situation where a missionary costs 800 faith and a prophet costs 900.
Consider that prophets are more powerful than 2 missionaries but also consider that you don't want to take prophets too early. You'd want to take advantage of the lower cost of missionaries when they are still cheap.
If a city isn't religious or has just a few followers you can use missionaries. If you want to convert a major city with 20ish followers then a prophet is better.
I personally build an inquisitor only in the following 2 cases:
1) My neighbor is aggressively trying to convert me.
2) I conquered a city with more than 10 followers of another religion or an holy city and I want to convert them in one go.
Itinerant Preacher is actually stronger than religious texts, until you get the mid game tech that buff religious texts. After that it's a lot harder to say what is stronger.
I've made several tests, including playing hot seat with myself taking IP with one civ and RT with the other.
According to my findings when cities are closely packed together the two beliefs are almost equal
before printing press.
It is true that IP influences cities further away, but a 12 influence does nothing if that city has +48 from its main religion.
Meanwhile with printing press you might not have influence at all with that city further away, but you'll have stronger pressure on the closest city so you'll have better chances at converting it and faster. Once converted then you'll still reach that city further away but with stronger pressure.
In other words a focused conversion on closest cities is better than a weaker conversion on a larger area.
There are however exceptions to this rule, and that is the case with sea based maps, where you might not have closest cities at all and therefore it's better to spread your religion further away than not affecting anything at all.