It's difficult to say because it matters on your criteria. I would completely disregard starting position because it's so easy to pull off a 'barbarian migration' (in my current game as the Turks, I abandoned all starting provinces and took control of Crete, Rhodos and Cyprus. Thanks to the island bug, I had no worry of being attacked and could develop my economy. Best campaign yet). Likewise, comparing only the best units disregards availibility, since you'll likely fight the first 50 or so turns with mostly crappier units.

All italian factions have a super advantage in their militia troops, but despite that I'd pick the Moors. Why?

Infantry: Dismounted Christian Guard is actually better than most dismounted knights. Also the Urban Militia is a great militia unit. However, considering that both of them are somewhat elite units, the overall rating for Moor infantry is average. They have decent spearmen but nothing impressive and until you get the better units, you'd better not rely on infantry to win your battles.

Archers: A poor selection, definitely the Moor weak spot. However, the basic Desert Archer is decent, with both long range and good stamina. Like their basic infantry, not much to rely on but they get the job done.

Cavalry: A very good selection ranging from the basic Arab Cavalry and the city-recruited Tuareg Camel Spearmen, to the Granadine lancers and the Christian Guard, which is equal to the Templar/Hospitaller Knights. They also have spear-throwing cavalry which is great, the fast-moving Granadine Jinetes is probably the best such unit in the game.

Also, one thing which I consider to be very important about a faction's cavalry selection is the availability of at least one fast-moving unit. The lack of such is IMHO very negative, which is a major reason why I'm not too fond of neither England nor Poland.

Gunpowder:
Quote Originally Posted by PaulTa
With the advent of gunpowder, you can produce Cossack musketeers, the second best gunpowder unit in the game. You also have something those Turks who stole first place don't have[...]
Dear Sir, I think what you really meant was third and second Because the best gunpowder unit in the game is the Moor Camel Gunner. Hands down. It's the gunpowder equivalent of the horse archer with all the advantages of the latter combined with the wonders of gunpowder. With long range. And as if that wasn't enough, there's the camels. With the 'freak-out-horsies' bonus. This is the ultimate morale killer, easily able to take out any knights sent after it. It has no equal. There is no army I would rather have than one filled with these guys, backed up by some Christian Guard and Granadine Jinetes. Also there's good artillery(cannons) and better-than-average arquebusiers in the Sudanese Gunners.

All in all, the fantastic later-game units of the Moors more than compensates for their poor earlier units. And that is why, IMHO, the Moors are the most powerful faction in the game. The muslim advantages of Jihad doesn't hurt either.