Their weight is exactly the same. A pound is a pound. Assuming both are weighed using the same scale, troy or avoirpudus.
For further commentary along these lines I'll go on a bit about weight and mass. When we casually, (in everyday use), talk about weight on Earth we actually mean the mass of an object. Mass being a measure of the absolute quantity of matter in an object.
On Earth one pound mass equals one pound weight. This is only so because the standard unit of weight, a pound, was defined and calibrated on Earth. Weight is actually a measure of the amount of force a body exerts on an object. That force is dependent on the amount of gravity the object has, hence it is dependent on the size and mass of the body creating the gravity. (Gravity being defined as the curvature of space around an object. The whole topic of gravity however can be expanded on to death)
On other planets, celstial bodies, spaceships, etc. one pound mass does not weigh one pound. The moon is a common and great example of this. Having 1/6 the gravity of the Earth, it would require 6 pounds mass to measure a weight of one pound.