Turks and Eggies are indeed great when you play every battle yourself. Their superior mobility and firepower ensure a minimal casualty victory - along with some micromanagement. I also got the impression that generals level up somewhat more quickly than Catholic ones because many Muslim troops are assessed as inferior by the game (see below), meaning that the achievement is greater when winning with them. This leads to the next point....
Due tho this, in autocombat their troops are crap IMHO whereas it works quite good for Catholics.* I suspect that missile capability isn't counted in AI combat balancing / autoresolve (at least that's the case in RTW), so their numerous missile and hybrid troops suffer. Since I've come to enjoy autoresolve more than once in a while, embarking on a campaign as Turks or Eggies no longer is a realistic option for me, notwithstanding the fun of playing them.

*edit: partly for the Byz as well, often purely horse-archer armies were easily defeated by byz inf in autoresolve whereas they would have been shot to pieces had I commanded the battle myself.