Let X and Y be compact Hausdorff spaces, E a Banach space, and C ( X , E ) C(X,E) the space of continuous functions on X to E. E has the weak Banach-Stone property if, whenever C ( X , E ) C(X,E) and C ( Y , E ) C(Y,E) are isometric, then X and Y are homeomorphic. E has the Banach-Stone property if the descriptive as well as the topological conclusions of the Banach-Stone theorem for scalar functions remain valid in the case of isometries of C ( X , E ) C(X,E) onto C ( Y , E ) C(Y,E) . These two properties were first studied by M. Jerison, and it we later shown that every space E found by Jerison to have the weak Banach-Stone property actually has the Banach-Stone property, thus raising the question of whether the two properties are distinct. Here we characterize all three-dimensional spaces with the weak Banach-Stone property, and, in so doing, show the properties to be distinct.