The only reason i would disagree is that in the cold war you didn't have active proxy wars going on and the circumstances here are wildly different.

The thing here is we know Iran is backing the Iraqi militias/Assad/Hezbollah. Those are its natural ally's they aren't hiding that, Saudi Arabia is supporting various groups as well so is the rest of the world. I will exclude the Houthis because the link between Iran/Houthis is very weak compared to those others, Iran does try and help them though but they are Shi'ite and Iran is claiming to be the leader of Shi'ites and all so it would be in its interest to help them somewhat.

Saudi Arabia is sponsoring Wahhabism openly, they claim they aren't like ISIS though but that's fucking bullshit and if i have to explain why whoever doesn't know needs you use the almighty Wikipedia or Google. Out of context the seems irrelevant but in the middle east its very relevant. This is only if you decide to draw the lines based on a religious motive (Not wrong but usually countries will never go to war only because of religion, even during the crusades it was more then just religion)

If you want to forget all that and think like a Saudi King, What the hell would you gain by going to war and losing money, possibly even power? Saudi Arabia isn't playing the proxy war game and trying to keep the chaos out of its country cause they're warmongers. They already have lots of influence and generally probably don't care about Iran, they are probably more concerned with how to keep itself in the Wests good grace while keeping the far-right attitude going...

This is just the few shot things i can come up with but hopefully you get the point. In my opinion we will probably never see a Iranian-Saudi war because its A) Useless, its no longer 1,000A.D you can't go around pillaging and looting after conquering land lol. B)The world simply won't allow it without all hell breaking loose. C)Both Iran and Saudi Arabia share a mutual interest in staying as strong as possible. D)People are fucking tired of war...that's mostly just me though i think.