I've heard the comparison that this group is the same kind of caliphate style setup where they wear white instead and stability is granted through oil and money.
However, I don't know how accurate such a statement is. I've also heard SA compared to a bunch of tribes that are continually bribed to behave cohesively.
It is accurate. Daesh follow wahabism, the Saudi branded form of Islam that is much more extreme as did Osama Bin Laden. The HuffPo isn't my favorite news source, but this is a good article:
It's a mix of Sururiyya, which is influenced by Wahhabism and Ba'athism where a state is ruled by a vanguard party. They removed the disloyal parts of Sururiyya which called for questioning inept leaders and replaced it with the unwavering loyalty obligations of a typical Ba'athist dictatorship.
The fact that Saddam era henchmen who clashed with KSA over the pillaging of Kuwait are running Daesh, plus the propaganda coming out from them calling for the removal of the house of Saud as custodian of the two holy mosques, and considering Saudi military defectors and political dissenters make up the majority of Daesh recruits it seems suicidal they would support them in anyway. Maybe there are political opposition in KSA doing so but even that would risk their own status since Daesh proved they don't care about agreements when they invaded Mosul and promptly executed the local elite who helped them get in.
However, I don't know how accurate such a statement is. I've also heard SA compared to a bunch of tribes that are continually bribed to behave cohesively.