Get small amounts of both materials and see which techniques you can learn faster or master. Both are suitable, it's more about how you interact with the materials.
- don't try to carve the ball or boxes, use things that come in those shapes.
- use wire or dowel pegs to attach your segments together, don't rely on glue between flat surfaces. Especially the handle into the cube!! Must penetrate to be a substantial handle.
- the prop you linked is by a very highly skilled person, dare I say a Master Craftsman. Yours will not likely look nothing like that.