For some reason the Fatimids have a lot of good bonuses at the beginning of the game that just make them way too powerful without some modding (and even with modding). Basically:
1. The Fatimid Caliph owns a large number of counties at the beginning of the game, and he can also easily make a few duchies, too. He ends up giving the counties and duchies to his vassals and courtiers...
2. Vassals and courtiers of which already like him, because of his decent traits and stats. So now they love him more and never bother to rebel or launch faction wars (unlike with the Seljuks).
3. They control the Mamluks. They basically get a free uber-powerful holy order-mercenary group that's several thousand in number at minimum.
4. They can quickly holy war Nubia and Ethiopia, as well as their non-Shia neighbors, earning more piety - not that they weren't gaining a lot of piety in the first place, anyways. And then they use this piety to holy war more people and go on invasions and Jihads.
5. They own some of the wealthiest cities in CKII's world, including Alexandria and Cairo. So they roll in cash. Which they use to build more soldier-producing buildings.
6. With increased piety and cash at hand, they can also easily lower decadence, reducing the chance of dissatisfaction by vassals (not that it would have mattered much, given (1) and (2)).
Among a few other things I don't remember. So basically, the Fatimids are a big happy family rolling in gold, piety, and great units.
I've heard in some places that the only non-player AI that can stop the Mongols and the Aztecs unscathed... is the Fatimids (or their decadence revolt successors).
Personally I've made a mod which introduces some hefty measures to reduce the Fatimids' power, and even with that they still manage to remain relatively strong. I just don't understand it. It's like they're superpowered human-robot-aliens or something.