I'm no expert, but the rulers of Jordan are the Hashemites, the family that had responsibility (rulership) for both Mecca and Medina, before they were driven out by the Sauds, who were then installed as the rulers of Saudi Arabia by the British after WWI.
The Hashemites, I believe, have a direct lineage to Mohammed, the Prophet, whereas the Sauds do not.
I also read something about the House of Saud being part "Westernized" and part "Wahabist" (sic).
Some of the Saudi Princes have spent considerable time in the West, such as Prince Bandar, who was the Saudi Ambassor to the US for many years.
Others have spent very little or no time in the West and are old-line Princes of the Desert.