By means of numerical simulation, a comparison is made between conventional spectral phase interferometry for direct electric -field reconstruction (SPIDER) and delay-controlled fringe-free SPIDER (DCFF-SPIDER) in the accuracy of characterization of complex pulses. The results show that errors occur likely when complex pulses with abrupt variations in spectra or/and phases are characterized with conventional SPIDER, while DCFF-SPIDER can give high accuracy. The underlying reasons for this difference are discussed.