Could you post an orthographic render of the same picture ? The perspective view makes us view your sphere at different orientations between the three views.
I think it is because normal maps modifies the shading but not the topology of the meshes, you should get the same silhouette for the three spheres in orthographic view. You’ll have to subdivide more if you want it gone.
Ok, it’s a geometry problem. I had some hopes there were means to get a good looking result without adding faces (which is one of the reason to use bump maps after all) but apparently it’s not possible.
I’ve looked better at the results and actually the middle result (with the smooth shading) looks nice but is completely wrong. It suffers from not enough faces too.
It’s easy to spot on the follwing test. The second range is Gimped, I’ve added the middle shadows on left and right results and it’s obvious it’s wrong. The shadow area is much too big and looks weird especially on the right result.