which is cheaper a worm gearbox or hellical gear box?

Don't know exactly what application you're referring too, but it's kind of a trick question. A helical gear is in fact called a worm gear when it's teeth are fine and it's used to drive an annular gear (like an old steering gear- NOT rack & pinion). Usually they're called a helix gear when the teeth are coarse and it is meshed with another similar helical gear, such as in a helical gear pump (common in industrial hi-volume oil pumps, or low-profile automotive supercharges like those made by Eaton corp).