Well, from my understanding, at least, a direct war between the two wouldn't be very likely. Pretty much up until the US left Iraq, the Iranians had no way of even getting to the Saudi border, so, as has been said, the war would pretty much have been at sea. And neither the Iranian nor the Saudi navies are all that amazing. I dunno, maybe the Iranians decide shut down the Straits of Hormuz for some reason, resulting in the Gulf Arab states declaring war? In that case, I imagine that the US would have done the heavy lifting and would have cleared out the Iranians.
And even after Iranian influence started growing in Iraq, I doubt the Iranians would have been able to just march a full on invasion force through there to hit the Saudis. At most, you'd have proxy warfare between the two nations, which is more or less what's going on now.