To give them their due, Arabian perfumery goes back millennia, they've been selling perfumes (frankincense, myrrh, and more) since before the Roman empire. French perfumery is much more recent, three or four hundred years, and real french perfumery started in the late XIX century (before that, it was simple essences of no consequence).
For the little I've smelled of Arabian perfumery, it seems to me they excel at simple accords with superb materials, in oil: oud rose being the most famous, but also jasmine, dark musk, sandalwood, saffron, and ambergris. They also excel at perfuming via smoke (again, wonderful ouds and resins). Hedonist will be able to say more here.
I do not think that, overall, they have mastered the alcohol form yet, nor have they shown huge interest in developing complex synthetic-natural mixes.
French perfumery, as I see it (and following Luca Turin's analysis), is based on natural synthetic mixes, where an abstract structure (chypre, fougere, etc.) is overlaid with naturals that give body and richness. Of course, IFRA has attempted, among the utter disinterest of the French, to destroy French perfumery by forbidding most natural substances (oakmoss, jasmine, eugenol, heliotropin, etc etc).
Hard to choose for me. Some oud-roses or jasmines I have smelled from Arabian perfumes are heavenly. But so are many Chanels, vintage Guerlains, Piguets, etc. etc.
Rose is typical of both traditions (the famous Taifi rose for Arabs), by the way.