While the cost of propane locally obviously plays into this, a propane dryer will usually be less expensive to operate than an electric dryer.
Its important to note that there really isn't anything very efficient about how a dryer operates. In fact, Energy Star doesn't even rate dryers for this reason. What does play into the effciency question however, is the washer. Higher efficiency washers take more water out of the clothes -- which means the dryer doesn't have to work as long to to dry them.
Also, keeping the dryer vent clean can shorten the drying cycle and prevents dryer fires.