Hard call. I'd say by default it will be white peace. So what matters more is that who would win in a long, brutal, zero infra war. Interestingly, if the question was US vs Iran on Iran home soil, I'd bet on Iran. US doesn't have very good odds of invading Iran without Saudi help.
First, it depends on what exactly you mean by no allied help. Iran has world class homegrown military tech. Without being able to buy allied weapons, Iran wins easily. With allied weapons purchase, Saudi has the cash to get some good American weaponry.
Saudi appears to have better military tradition. Soldiers are a part of their lifestyle; they have no police. And they have had some recent military conflicts, although nothing huge.
But what really matters is how long they can keep the war machine going. Saudi's economy is more unstable, 90% reliant on oil and tourism (pilgrimages). While Saudi is self-sufficient on many parts, Iran has more fertile soil and variety of resources. If both sides face embargoes, Saudi would be completely fucked up. Saudi also has a larger % of economy dedicated to military. Although both maintain about the same size of forces, Saudi's military budget is 8x higher.
So my bet would be on Iran.