I don't know either.  We have the formulas for each, so we can calculate squared error vs. sinc(x), but there also appears to be differences in which frequencies the distortion occurs and some could be more audible.

It occurs to me that there exists one very obvious function for which the squared error is minimized for a 4-point interpolator. 4-point interpolator impulse functions have to be 0 outside the interval [-2,2].

So, E=|f(x)-sinc(x)|^2 is minimized when

f(x)={sinc(x) -2<x<2 , 0 elsewhere

Note that since the Fourier transform is isometric and linear, we know that a function which minimizes the error in the time domain also minimizes error in the frequency domain. This spectrum ought to have a lot of ringing in the upper frequency range, and in the stopband.

So, if we only considered the squared error in the reconstruction and not the smoothness of the result, this would be the clear choice. How would we factor in the smoothness as well?