Count those tiles! From a defensive perspective, it's only if the distance between your outlying cites is between 11-13 hexes that IP is better than RT. (OTOH, I prefer 5-6 tiles between cities, so that IP difference can very important to me.)
If you have all cities in a straight line, IP will double pressure, against +50% with RT (and printing press) because your IP cities 12 tiles away will put pressure on cities they could not with RT. If your cities are set more organically, you're likely to get many more. cities between 11 and 13 tiles away from any other city.
For spreading outside your empire on your starting continent, yes, IP is almost certainly significantly stronger than RT. But if you share the continent with even one AI that takes its religion seriously, my experience is that neither IP nor RT will have significant effect.
I don't consider either that good at the initial spreading, which is best done by missionaries. Waiting for the first cities to flip is pretty slow without manually spreading. If waiting for religion to spread, if it is better to get the bonus strength from texts to get the first cities to adopt faster or influence more cities is pretty much a tossup in my mind.
I feel IP puts more pressure on civs that spam missionaries, because you might get up to 3 or 4 times as many cities applying religious pressure. If I take a prophet and bomb cities on the back side of their civ (either a religiously neutral neighbor or converting his cities), the long reaching effects of IP can put significant pressure on their cities.
Over the course of many MANY turns, I was once able to flip Thebes to my religion (it was the holy city of Islam, of course) though pressure from myself and Egypt's other neighbors, without manually converting even one of his cities, and those extra 3 spaces meant a lot to getting his satellite cities converted.
That is opposite of my experience, as I think most maps (that is, anything other than Pangaea) favor RT over IP. As compared to GnK, RT beats IP because of trade routes, where RT provides 50% more pressure (and IP has no effect). Trade routes can be used for CS conversion quests, saving you a GPr burn. If you have a city further than 13 hexes away, internal trade routes can keep them converted.
If you plan to fill out Piety and thus to make use of Religious Tolerance for the second pantheon belief, RT is terrific for managing those.
I rarely use trade routes for religion, I must admit. However, I can use trade routes to influence cities further away while my natural pressure influences those 11-13 tiles away from a city, so, again, it effectively doubles the pressure I can create with one city and one trade route (this effect is obviously lessened in wide empires and even better in all empires where there will be several trade routes per city founded.)
I usually end up founding late, and still often have my pick of both RT or IP (when I would pleased to have either)! What is up with that?
I agree. The AI doesn't seem to like it. I believe they get reduced cost on faith purchases though, which could make other beliefs look better for them. More goodies for me though
I have yet to have that one available, but it does seem very good. Cheaper GPr is my third favorite, and also excellent.
I'm just coming around to liking cheaper (or more points toward) great people as an amazing thing. I'd like to try that belief some time now, but I've yet to come up with a map where it looked good. I would consider it more late game. Around the industrial or atomic era, missionaries get too expensive, and a prophet or two can blow another religion off the face of the earth for good, so...on my to do list.
The CS never seem close enough to my core territory that I have been able to make RU work. But mostly I play the Continents Plus script, and one of its effects is to make the CS significantly more remote.
If I find a small continent with 2-4 CS all within 10 hexes of each other, and convert them all, would RU have its full effects even though none of my cities are in range? That is, does RU cause a CS with my religion to exert double religious on other nearby CS?
I don't really understand your emphasis on spreading your religion. You seem to imply that IP versus RT makes that straightforward. Further, you imply that want to keep the CS converted, when I feel the opposite is actually true (because the CS conversion quests can occur multiple times a game for the same CS).
I normally use continents (though I have mixed it up more recently, playing against a civ's strengths before moving up a difficulty level), and the result is often groups of CS's, or at least pairs. They aren't often that close to me (except 1 pair), but that is part of the beauty because, yes, your religion spreads to CS's at double rate, from any source. A core of 3 CS's far from me will often feed enough pressure into itself that I don't have to try to keep them (unless a prophet converts them, but then their next one is more expensive and they are easily converted back by missionaries) while also exerting pressure for my religion on surrounding cities (often enough so that even fairly late into the game, missionaries can convert them without much effort).
I don't think any religious beliefs make spreading a religion more straightforward. In fact, my personal emphasis on spreading religion speaks more toward my follower belief choices than anything, as I don't want to lose the religious war on one front and give buildings to a civ, and I put more faith into spreading my religion, so the buildings slow me down in that crucial time.
The reasoning behind it is mostly diplomatic (though, culturally, it can help as well), but it has nothing to do with my enhancer really, just the slower decay on CS allies, more friendly AI's toward me (and fewer toward other AI's), and the possibility of founding the world religion which can really push me to the forefront of world politics in the "world industrial era" (aka, when I research radio, there's rarely more than one world congress vote before that.)