Zombies are tangible beings because they are just infected human beings (for the most part, depends on the mythos). A haunting implies the presence of a supernatural entity and because of this the antagonist seems far more difficult to understand, especially fight. At least zombies can be killed by destroying the brain or brain stem, but ghosts/demons/apparitions on the other hand are untouchable and generally defeated through ceremonial means (which is difficult to figure out). Plus, a ghost can follow out outside of the forest and stalk you indefinitely. Zombies are limited by their own physical rotting bodies.
Attempting to travel through a zombie infested forest would be scarier. If a zombie scratches/bites you, you become one of them, you might go on to kill your loved ones. If you traveled through the forest with a group of people and someone else got infected then you would have to kill them in order to keep the entire group alive. Having to killed one of your own is worse than if ghost's attacked and killed (since there are no side-affects).