I've got a crossbow w a red dot sight. The rate of fire is way slower.
In the time it takes me to nail one zombie in the head w that, recock and get off another shot, I could nail 3-5 with this Mongol bow.
OTOH, if you don't have the experience w bows I do, the crossbow is the better choice. The avg person is going to be able to make head shots w a crossbow way easier w way less practice.