My arm chair perspective on the Saudi Arabia / Iran beef.
KSA (Kingdom of Saudi Arabia) has had it's coming out party this past year. It's no longer just playing in the shadows with Jihadis and stirring up sectarian rifts. It's pounced on several opportunities (Syrian revolution, Iraq's Shiite revenge killings), but is also trying it's hand at being more overt, primarily with it's involvement in Yemen. In the later it is always trying to claim that the Houthi's are Iranian backed, to the point where it's the standard narrative in the US. It's getting more and more difficult for KSA to claim any success in Yemen despite dragging in several gulf states along with it. It mostly just looks like what it is, a humanitarian catastrophe. Their proxies in Syria are also failing. The Free Syrian Army is increasingly behaving desperate and radical under the sheer weight of Russian intervention. Less significantly, energy profits for KSA are way down. They are under bidding oil prices just to maintain market share. To offset this KSA has been taking on sovereign debt for the first time in almost a decade.
Meanwhile Iran gets to claim many political victories as of late. Syria regime aside, they have just complied with the IAEA in turning over their enriched uranium ahead of schedule and big players will become willing to work with them. They are also the only regional actor, aside from the Kurdish groups, willing to build a coalition of militias to take on ISIS from the East.
Iran's weakness is appearing as a protector of the Shiite world. Not just because of it’s Shiite spiritual leadership, but because of it's support of Syria/Assad and his Alawite benefactors. The Assad/Russian airstrike massacres have alienated a lot of people. Even Hezbollah is retreating back to Lebanon stating that it has it's own priorities.
It's worth noting that both KSA and Iran, demographically, have peaceful coexisting populations of both Sunni and Shiites (and Jews and Christians in the later). It's analogous to American conservatism: no one really cares if you are protestant or catholic. It's unbelievers who distrusted in this country (according to polls). The same is true of most of the muslim world. If you have a moral center based on faith, most don't care about the particulars (Even the Afghan Mujahideen saw their war as against godless foreign invaders). Sectarianism has developed as group-identity in the threatening power vacuum left behind in the wars. It's those in power that leverage this divide to legitimize their own enterprises.
The KSA might not be sophisticated enough to have executed Nimr al-Nimr as a political antagonism. They had, at the same time, executed actual terrorists, the men who bombed the Shiite mosques in Saudi Arabia in 2003. But it seems they didn't want to rock the boat too much and thought killing a prominent Shiite cleric along with some Salafist radicals would make their capital punishment appear unbiased. This is very typical of clumsy KSA mentality and it backfired.
Even though al-Nimr is Saudi (and not Persian), he was popular in Iran's revolutionary culture (he studied there). It’s also a popular narrative that the Saudi Kingdom likes to mettle in everyone’s business (muhc like they assume Israel does). Therefore it doesn't strike me as government involvement that a bunch of Iranians went and ransacked the Saudi embassy. The government is already trying to reign in those who were involved.
But it might be a moment of KSA opportunism to sever diplomatic ties with Iran over this. This is how the new and improved Salman monarchy operate. Go big, be even more absolute than Abdullah.
My point is this: Increasingly Iran is the authoritarian stabilizing state (like their Russian friends) and Saudi Arabia is the authoritarian destabilizing "venture" state (like their American friends).