The blue curve is not ‘shifting’. It has a different scale with respect to the independent variable than the purple curve. The correct way to characterise it would be to compare the characteristics of the two curves.
For example —
x = linspace(-100, 100);
yb = 1./(1+exp(-0.1*x));
yp = 1./(1+exp(-0.05*x));
ratio = mean(gradient(yb)./gradient(x)) / mean(gradient(yp)./gradient(x));
plot(x, yb, '-b')
plot(x, yp, '-m')
Here, the ‘ratio’ metric compares the means of the numeric derivatives (calculated by the the gradient function) to characterise them. I am certain there are more appropriate metrics for your curves, however something like that would likely be more appropriate than measuring a ‘shift’ that is actually not a shift.