Hussein was Sunni as well, as I recall.
It’s well known in the muslim-arab world that Saddam & his Ba’ath party followed an ideology mixing Arab nationalist, pan-Arabism, Arab socialist and anti-imperialist interests. Ba’athism called for unification of the Arab world into a single state. Its motto, “Unity, Liberty, Socialism”. That has always been in direct conflict with Saudis strict Wahabi Islam. Moreover, Kuwaiti leadership is related to the House of Saud. Am sure SA is very capable of defending itself. But they won’t take overt & direct military action unless IS or another entity directly attacks SA territory, the House of Saud & their Islam, which they’ve been keen to spread around the world.