It is interesting to look at how the auto-routing performs in Diptrace. Attached are the following:

(1) My 2 layer hand routing, with as much ground plane fill on the back side as I could do. I tried to do as much of the routing as possible on the topside so the ground fill would cover as many things as possible.

(2) The auto-routed 2 layer which doesn’t have any planes. The autorouter uses a pretty simple layer direction method, with more traces on the lower layer than the upper one.

(3) The auto-routed 4 layer with a ground plane fill on one inner layer, and a power fill (both 3.3V and 5V, with the 3.3V parts on the upper part) on the second inner plane. After adding the fills I let the auto-router do the rest.