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.