The displacement behavior is dependent on the object's scale. First thing to test consistency is ensuring the scale values 'applied' either by clearing transforms (with ALT + S) or applying transforms (CTRL + A ---> Scale). My guess is that your objects have scale transforms that are causing different results with the wave displacement.
Good rule of thumb: If geometry-based tools/operators/modifiers/shaders are doing weird things, check scale values and clear or apply them.