Perceptive readers have noticed that I like Islam. Before explaining why, do the following: Forget about current events. Go back around eight hundred years, when the Christians were butchering heretics and the Muslims were inventing algebra. Also, keep in mind that my liking Islam does not mean I think it's true. I'm talking about an aesthetic appeal.
1. Islam is focused on the main point.
Muslim's are fanatically anti-idolatry. No icons, no pictures of Muhammad, no nothing. That's why Muslim art is mostly calligraphy and flowers, not Jesus getting crucified (gross) or grotesque Where-the-Wild-Things-Are-type godlets (think Hinduism).
When Muslim's pray, they face the Kabbah in Mecca. It's just a big black square rock, which they claim Daddy Abraham erected. Unfortunately, they idolatrous pre-Muhammad Arabs later put idols around the Kabbah, but Muhammad got rid of idols and reminded everyone that the Kabbah is where it's at.
This is kind of like what the Rebbe says in "B'yom Ashtei Asar": forget the BS. Remember the ikkar.
2. There's less of a "yeah right" reaction
Face it. There's some stuff in Judaism, to which the natural response is "yeah right." I like to minimize the public kefira, so I won't go into examples. Christianity also has lots of "yeah right" doctrines (virgin birth, infallibility of the Pope, "No man cometh unto the Father except through Me," to name a few). With Islam, you have much fewer. The Koran was written recently, so it's not hard to believe that it was actually dictated by Muhammad. The Koran doesn't include a hard-to-believe-ancient history. So believing Muslims don't need to argue with mainstream scientists and historians.
3. There's less "crazy stuff."
Judaism has lots of crazy stuff, eruv tavshillin, kappores, sha'atnez, wacky holidays, etc. And we also get really OCD. Open up a Shulchan Aruch and you'll be amazed at what the rabbis think up. Muslims have "normal" rituals (relatively). No crazy long prayers that are impossible to pay attention to. No writing scrolls that nobody's gonna read (think tefillin and mezuza). No refraining from electricity to help you "rest."
I don't know if this really does justice to issue. I think there's a more underlying and more essential property of Islam that appeals to me, but this is the best I can come up with.