I have read about the Iran-Saudi Arabia proxy conflict and I would like to know who has more regional influence in the Middle East in terms of political and cultural influence, Iran or Saudi Arabia?
Saudis have the power of the purse, but Iran commands more respect
Theoretically speaking, Saudi Arabia should have much more influence. They have much better economy and living standard, they are custodians of Muslim holy sites, they are Sunni (majority of Muslims) compared to Shia dominated Iran, their military is much stronger on paper and they are not isolated by the West (in fact they have very good relations). However, lots of this is just a facade. Saudi economy is still reliant almost exclusively on oil, and they are practically unable to produce much else. Although in public very religious, it is long rumored in Middle East about promiscuity and other vices of Saudi princes. Military is mostly made of foreign mercenaries and as witnessed in Yemen recently, not very good, to say the least. Finally, politically speaking, Saudis are often viewed as mere lap-dogs of the West, especially United States. And considering US-Israeli firm ties, Saudis are by extension allied with much hated Israel. To sum it up, Saudis are rich, fat and spoiled kid, one that prefers to bribe other to fight for him, because he is too soft to do that on his own.
What about Iran ? Iran is comparatively poor, isolated, Shia, on the surface more liberal and generally appear weaker. However, Iranians have their own industry and technological base. Despite all the sanctions they have developed pretty good military technology, especially missile technology. Iranians managed to down US drones, precisely strike Saudi oil refinery with cruise missiles (probably with the help of their proxies in Yemen) and now even retaliated for the killing of their general with surprisingly accurate ballistic missile attack on US base. Bear in mind that in few decades before, US and Israelis trashed practically any Middle Eastern opponent (except Hezbollah, supported by Iran) . Now it appears that US would not continue with military escalation against Iran, which is practically unprecedented in modern times - and this gives Iran huge dose of prestige in Middle East and whole Muslim world. This could be only enhanced if Iran manages to develop nuclear weapons (second Muslim country to do so, after Pakistan) . In other words, Iran is like poor but proud man, well versed in combat, and ready to speak his mind no matter of consequences.
In the Middle East, there is a saying, Saudi buys its allies, but Iran allies are brothers in arms.
Saudi, being an absolute monarchy, their at most goals is to stay as such. by allying with the west and doing their bidding in the area. you do not have a dogmatic reason to ally with Saudi,
Iran, on the other hand, have Islamic dogma, opposition to the US and Israel, which gives her a lot of support and friends.
They also treat their allies better and stick with them, Saudi is known to be inconsistent policies, switching sides rapidly.