honestly besides diplomatic victory I see them as unnescessary.

what are the pros and cons?

If you want only war then they aren't all that good especially the U.N. since it can let someone else win and take away your ICBMs but the A.P. can stop trading with your enemies so it can still be useful.

The AP gives you +2 production per religious building so it is useful beyond the diplo abilities. This can be especially useful in GP farms with very few production tiles. +2 for temple/monistay/cathedrial that stacks for a total of up to +6 (plus modifiers from forge etc.).

If possible, it is best to build both of them even if you are not going for a diplo win. That prevents the AI from building them and controling the votes.

The AP is useful for the hammer bonus, and occasionaly for dogpiling on an AI.
My games are usually over before the UN comes into play.

I like it in the sense that it helps give a greater sense of a global community, instead of it just being me against the world.

Late game alot of AI's adopt a SE for some reason. Forcing US and emancipation can really mess them up.

The biggest annoyance caused by both of these wonders is that the AI will use them to stop your wars if you don't control them. So either control them or raze them.

Why you want the AP and/or UN other than a Diplo win. I will talk about CONTROLLING" each rather than simply buuilding it

AP:
1) You are guarenteed a +2 hammer bonus on each religious building of the AP faith
2) You can initiate an economic blockade on the tech leader IF they do not have AP faith.
3) You can get yourself out of a bad war.
4) You can reassign cities to other AIs to screw with them. This is often defied causing excessive unhappiness.

UN
1) Ban Nukes.
2) Extra trade routes and forced open borders which help commerce and teching for a space race.
3) Forcing certain AIs out of their favorite civics to "Stir the Pot". Forcing certain leaders out of theocracy, Bureacracy, HR can have dramatic diplomatic consequences.
4) End annoying wars while targeting peaceful victories.

in my experience, the AP options do offer a nice variety of resolutions to vote upon...
some of the best include *stop trading with X*, and *declare war on Y*- getting the AP allows you to put forth those resolutions, the great thing about these two as well is that they are rarely defied, so if you have a majority you can get it passed..these add up to useful diplo bonuses such as shared military struggle...basically the AP serves as a massive unifier of the people of the faith..all acting to one decision, the shared bonuses stack up over time quite nicely.....

imho, the stop trading option is brilliant since it can basically knock one civ out of the game (with no open borders its pretty difficult to stay in the tech game for most civs)
oh....all of this means i'd much rather control it to get the resolutions i want....rather than what the AI wants.....i rate the AP much higher than most other wonders..its in my top third of wonders i want lets say.

Can anyone confirm this? It seems to me that when I build the AP it is easier to bribe/spy AIs into the AP religion and keep them there. Granted it doesn't help with fanatics who found their own religion, but it seems to do well with people with whom you might just need a +2 relations boost.

Another nice thing is that you can use them to get a +1 relations for voting for an AI.

For the UN other pros:
1. You can utilize some civics without anarchy. If you are planning on going FR anyways for tech/happy; you can avoid having to pop a golden age or anarchy by just voting it through.
2. You can utilize some civics without the correct technology. Most commonly I'm powerteching out for military techs and can't get my hands on ecology (because all the AIs hate me, I have nothing to trade, or I'm too advanced), but need the health bonus.

My personal favorite course is to build the AP myself so I can control it and the hammer bonus and then taking the UN from whichever peacemonger builds it. So long as I don't acquire mass media myself, I keep the AP bonuses and the UN ones.