We comparatively investigate the influence of various high-permeability alloys on the hysteretic and remanent resonant magnetoelectric (ME) response in a composite of magnetostrictive nickel (Ni) and piezoelectric Pb(Zr1-x, Ti-x)O-3 (PZT). In order to implement this comparative research, Co-based amorphous alloy (CoSiB), Fe-based nanocrystalline alloy (FeCuNbSiB) and Fe-based amorphous alloy (FeSiB) are used according to different magnetostriction (lambda(s)) and saturation magnetization (mu M-0(s)) characteristics. The bending and longitudinal resonant ME voltage coefficients (alpha(ME,b) and alpha(ME,l)) are observed comparatively for CoSiB/Ni/PZT, FeCuNbSiB/Ni/PZT, and FeSiB/Ni/PZT composites. The experimental data indicate that the FeSiB/Ni/PZT composite has the largest remanent self-biased alpha(ME,b) and alpha(ME,l) due to the largest magnetic grading of lambda(s) and mu M-0(s) in the FeSiB/Ni layer. When the number of FeSiB foils is four, the maximum remanent alpha(ME,b) and alpha(ME,l) at zero bias magnetic field are 57.8 V/cm.Oe and 107.6 V/cm.Oe, respectively. It is recommended that the high-permeability alloy is supposed to have larger lambda(s) and mu M-0(s) for obtaining a larger remanent self-biased ME responses in ME composite with high-permeability alloy.