The shape of a focus-modulated point spread function (PSF) is used as a quick visual assessment tool of aberration modes in the PSF. Further analysis in terms of shape moments can permit quantifying the modal coefficients with an accuracy comparable to that of typical wavefront sensors. In this letter, the error of the moment-based wavefront sensing is analytically described in terms of the pixelation and photon/readout noise. All components highly depend on the (unknown) PSF shape, but can be estimated from the measured PSF sampled at a reasonable spatial resolution and photon count. Numerical simulations verified that the models consistently predicted the behavior of the modal estimation error of the moment-based wavefront sensing.