After the Caesar comments, here are some more comments on other leaders.
I must first specify i usually play on european/asian-european maps, so i have more or less always the same leaders. Difficulty Noble/Prince usually, on large or very large maps playing epic games.
I just add unusual comment, won't say again about techies from England, Gandhi power builder etc etc...
Frederick
As i often play Russia, he is a common neighbor to me, and quite strange AI.
First, he globally does not really care for religion (opposite to Isabella on this point). I have often turned him to my religion while he was fundator of another one, not even by asking him, just by sending missionaries everywhere. He builds few missionaries, but if you give him some, he will use them, even on his other neighbors if all of his cities are yet religious. Very useful point to know.
As far as you trade with him and share religion, he never agresses you. Even if you refuse military askings or trade with foes (as far as it stays reasonable).
Even if you attack him at one point, you can quite easily befriend with him again later, if after the fight he his in a weak position, he will not hesitate to ask for open borders very fast (10 turns after peace).
In another hand he builds very quickly and uses chop. So a neighbor you need to dominate or really befriend quickly, if not he is a very strong opponent, even if not agressive.
Isabella
In EVERY game she HATES me. Every. No exception (well, i never share religion with her since both of use got one each time and none of us is agreeing to switch).
One game she asked me to switch religion something like in 1000 BC, i refused, she declared war. She NEVER agreed to make peace until 18xx AD !!!! (she would only sign peace treaty if i accept to give her something, what i would never do since i am quite sure less than 30 turns after she will declare war again...).
Every time, she does not offer border sharing as far as you do not share the same religion. A damn fanatic !
Mongols - both
They are fan of asking for bride. And often they are technologically back, they are warmongers (but chaotic ones, not organized ones), so often make war with your ennemies. If you from times to times declare war for him to a far ennemy or agree his blackmails from time to time, he can quite easily befriend. And it's quite a nice thing to have such a crazy man on your side, since he will easily declare war on your ennemies if you ask him.
Since they are back in technology, it's often useful to give them some, so they can be more annoying to your ennemies
Since they will probably not be a real challenger at the end, you can afford it.