Blocky lightning effects on smoothed model in Object mode (2.79b)

Hello, I am getting some blocky lightning effects on my smoothed model in Blender when I look at it in Object mode. I am following a tutorial on how to create a Lego-looking character that will be imported in Unity and I want to make sure that the final result will be good.

I am using smooth shade and auto smooth set at 78.6 degrees. Capture

You can see vertical and diagonal light lines on the cylinder shape.

Can you show the wireframe? Your object might just be too low poly to get smooth normals. Add some horizontal loop cuts near the ends to fix it

Here is the wireframe.

Perspective:

Front Orthographic:

I later created the same model in Blender 2.8 beta and it seems to look a little better but I do not know why. Picture from 2.8: