A fantastic blog from Daniel Jenkinson on the recent and historical tension between Saudi Arabi and Iran.
Sunni Muslims pitched against Shia Muslims. After Prophet Muhammad died, a branch of Islam was created (Shia) and thus the mainstream Sunnis were now contending with an 'offshoot' of their religion, though many beliefs and fundamental principles are identical.
In its most current and modern form: Iran was/is gaining influence in the region by it's (alleged) coaxing of conflict and tampering with the politics of other nations and this is worrying Saudi and they believe Iran will tear the countries apart and dominate the region. This is also the reason the USA has had to take increasingly powerful and more robust steps to curb Iran's nuclear programme - if Iran obtained nuclear weapons the general consensus is they WILL use them against the Sunni nations.
It is alleged, By Saudi and their allies (Bahrain, UAE) that Iran is trying to cause religious wars within these countries in the Middle East in order to push their own political agenda, by stirring civil wars.
Iran strongly denies this, claiming it is in fact Saudi doing the same - this stems from religious war - though compelling evidence is forming a substantiated and credible opinion.
Summarily, Saudi accuses Iran of trying to cause the Sunni countries to be torn apart by Shia rebellion.
The majority of Arab nations support Saudi as it is a most powerful ally to hold due to its strong support from the USA and the rest of the west, indeed.
Shia populations throughout the Middle East are seeking revenge and, whilst the recent executions might or might not have been on the grounds of counter-terror, there is plenty for the Shias to be upset with - they believe cold-blooded murder of their religious leaders (that are being 'targeted') is ongoing and, thus, Saudi is directly attacking the Shias.
This is likely to cause civil wars across every major Arab player; UAE, Jordan (already in progress), Yemen (already in progress), Bahrain (I've no doubt, soon to be in progress), Qatar (I've no doubt also soon to be in progress) and other nations.
The recent conflicts have resulted Iran being 'cast out' by way of the severing and downgrade of diplomatic ties, though Iran asserts it is, ultimately, the nations opposing it that will suffer the most.
Iran has a significant army, overwhelmingly larger in number than that of Saudi (though they spend considerably less on their forces than Saudi.)
If your mark of a strong country is how many troops it has, Iran wins hands down and dominates the battlefield in the game-of-numbers-sense.
In terms of numbers of followers, up to 90% of the world's Muslims are Sunni and 10% (est.) are Shia. The numbers are not favourable or even anywhere near balanced, but Saudi doesn't have nuclear technology.........Iran does.
To further compound with these problems: Iran supports one side of the rebellion in Syria, Saudi supports the other, namely pro-Assad and anti-Assad (though ISIS/ISIL has a very heavy following and many 'sympathisers' amongst the Shia community.