I haven't played as them much, but there are a few quite major differences when play as an Islamic ruler. Spain is a pretty good place to get to grips with them due to the close presence of both Muslims and Catholics.
1. Every (male?) character can go on Hajj once. Doing so gives you a permanent positive opinion modifier with other Muslim rulers and a small to moderate piety boost. You can also potentially gain a few positive character attributes and/or remove some negative ones. I tend to wait until I've developed at least one negative trait before setting off, but it can be useful to it earlier sometimes.
2. Piety is super mega important and can be used for imprisoning, declaring war and a few other things. You lose piety by declaring war on other rulers of the same religion.
3. You can hold both castles and mosques directly without penalty.
4. The only succession mode available is Free Succession. This means that whoever has the most titles will inherit everything and makes it pretty easy to choose your heir.
5. Decadence is a pain in the ass. You mainly gain it by having unlanded male family (including extended family) and lose it through observing Ramadan, granting land to family members and waging war.
6. You need to ensure you have enough wives for your title, or suffer a pretty major prestige penalty. This tends to result in loads and loads of sons who will plot against each other and you. You can bypass this to a large extent by marrying older women, but some may consider this twinky.
7. You have an automatic casus belli against any county directly next to your own, which is nice.
8. Women are pretty much worthless, so give your daughters terrible guardians to minimise the bonuses their husbands receive.
9. Whereas it's generally beneficial to spread your dynasty far and wide as a Christian ruler, Muslims have more to gain by pruning the family tree every so often. You REALLY don't want extended family coming into any significant power. Your family may well turn out to be your single largest threat.
10. Be prepared to be at war a hell of a lot. Expansion is much easier as a Muslim ruler, and rebellions seem a lot more common.
11. Keep your children weak, and your brothers/uncles even weaker.
