A circle in a square consumes more percentage of the area of the square ie., only 21.46% of the area is wasted.

On the other hand Square in circle wastes more area ie., 36.33%

For the circle in the square case to find the area that is wasted by the circle in the square in percentage we can use the following method

((s^2-πr^2)/s^2)*100

=(1 - (πr^2/s^2)) *100 ------ 1

but here

r=s/2

s=2r

s^2=4r^2

so 1 becomes

(1-(π/4))*100

=21.46%

Similarly in the case of the square inside the circle we end up with the equation

(1 - (s^2/πr^2))*100 ------ 2

but here

2r=(√2)s

or

s^2=2r^2

so 2 becomes

(1 - (2/π))*100

=36.33%

So we can conclude that the circular pizza consumes more percentage area of the square box it is in than the vice versa case.