Both are functionally dictatorships. While Iran does have democratic elections as pointed out above, the results of those elections are not always observed, as with this most recent Presidential election and the mass protests that followed. These protests were brutally repressed, with mass arrests and torture. Still, at the local and state level, elections are generaly considered to be more fair. One major difference with Iran is that it has religious leadership and political leadership, and the religious leadership is most powerful, so elected officials that openly defy religious law are arrested.
In Saudi Arabia it is a monarchy, isn't based on elections at all, but rather a family lineage. Now religious law is strictly observed in Saudi Arabia, with notable exceptions so that the Royal Family can stay in power and wealthy (not exactly central tenets of Islam). The elections there at the local level are pretty much dominated by men, and in some respects women have even fewer rights than in Iran.
I would define authoritarian government as one in which the government does not have to obey any (or many) rules. The government can act in any way that it wishes. It will generally try to repress its people -- it will take away their rights in order to keep itself in power or in order to maintain the system that it likes (regardless of what the people think). I think it is fair to say that both Iran and Saudi Arabia qualify.
In its defense, Iran is democratic to some extent. It does have elected officials. However, the last election showed that the people in power are not likely to allow the opposition to take power away from them. Iran also has an unelected religious leadership that can overrule the elected government. This religious leadership has imposed a certain set of rules (based on their religious values) on their people.
Saudi Arabia is perhaps less brutal with its people. On the other hand, it is not even democratic. It is a hereditary monarchy. In Saudi Arabia, the people have no say in choosing their national government. The government is also quite willing to impose its values. For example, women are not allowed to drive and are required to have male guardians who must approve of all their actions.
So both are authoritarian and both are somewhat of theocracies. Iran has more democracy, but Saudi Arabia is perhaps less brutal.
I would say that one primary level of difference between both nations lies in their relationship with the West. Of particular mention would be the United States. Since the overthrown of the Shah in 1979, Iran has had a very contentious relationship with the United States. The animosity between both nations has been present for some time. In his desire to consolidate power, the Ayatollah in overthrowing the Shah blamed Iran’s relationship with the “decadent” West as a reason why the spiritual cleansing of Iran was needed. In identifying the United States as a nation that is largely responsible for this, millions of Iranians began to understand the United States as a cultural and political threat to Iran’s leadership, in particular the Ayatollah and his interpretation of Islam. After this, much of Iranian leadership including the current leader, Ahmadinejad, have perceived the West in adversarial terms and are viewed by the Western nations in much of the same way. There has been little in terms of diplomatic or political gestures to bring a sense of common interest and globalized collaboration between both nations. This is not the state of affairs in Saudi Arabia. The United States’ constant and persistent dependence on oil and petroleum resources in the region have helped to cement a fairly stable relationship where both nations end up needing one another. Saudi Arabian interests lie in being able to broker the prices and need for oil upon which nations such as the United States are highly dependent. This collaborative partnership has been one to even trump national security. For example, an overwhelming majority of the hijackers on American planes on September 11 were of Saudi descent and there is quite a large al- Qaeda contingent and sentiment in the nation. Yet, American economic and geopolitical interests precluded an all out condemnation or demand for substantive change. Matters were handled quite diplomatically with high placed and sensitive discussions taking place. Consider for a moment if the overwhelming majority of hijackers of 9/11 planes were from Iran and how immediate the condemnation would have been. It is the nature of the relationship between both sets of governments and the United States leadership that provides the most amount of interesting divergence, in my opinion.