The Persian Gulf gives access to the Indian ocean, and through it to the Pacific, but the Med gives acccess to the rest of the Middle East/Eastern Africa and Europe without having to go all the way around the horn. It is rather important, and that access is one of the reasons that Iraq and Iran have been foes for so long. Additionally there is a nasty choke point on the Persian Gulf at the indian Ocean access point.

There are other ways that Iran can get to the Med, but the northern route is through some very nasty terain and several small unfriendly countries tha make a land-grab or negotiated treaties problematical in that direction.