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Saudi on the other hand is very "new" to the world in terms of culture and influence, only coming into prominence since the 1940s oil boom. The harsh environment isn't hospitable to living there without extreme energy use.
Both obviously have major regional economic power, but the Saudi society is built on sand (literally and metaphorically). In the very long term Iran's importance will come back so if anything the US and the broader world should be seeking to engage more with Iran and less with Saudi IMO.
That's not getting into a lot of the political stuff obviously, more just an analysis of the "fundamentals."
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That is mightily misleading. It is more important what part of the shiites make out of Middle East muslims. Because large parts of the muslim populations live in places like Indonesia, Malaysia, India, Pakistan, China, Bangladesh - and from bird's eye - they don't seem to care much about sectarian struggles.
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Also Saudi doesn't just follow plain old Sunni Islam. They practice Wahhabism (https://en.wikipedia.org/wiki/Wahhabism) which has a more literal reading of the Quran (which explains the higher percentage of extremism). The royal family leveraged Wahhabism to gain and keep power of the region.
As long as the countries remain governed by religious politics and inflict God's so called will on others, there cannot be an end to the conflict.