We compare here exchange bias (EB) properties of chemically synthesized core-shell nanoparticles (NPs), based either on a core of soft ferrite (MnFe2O4) or hard ferrite (CoFe2O4) protected by a maghemite shell (γ-Fe2O3). These NPs dispersed in acidic solutions are electrostatically stabilized, yielding to stable colloidal dispersions with a strong interparticle repulsion and negligible dipolar interactions in the probed range of temperatures. Field cooled (FC) magnetic hysteresis loops of non-textured frozen dispersions (with magnetic anisotropy axis of NPs distributed at random) and those of a powder based on the same NPs present a shift along the H-axis, expressing the coupling between the spin-ordered cores and the disordered surface layer of the NPs. The bias field is found to present a maximum, larger for NPs based on harder ferrite core. It is obtained for a cooling field of the order of one half of the anisotropy field, which is much larger for the CoFe2O4 cores than for MnFe2O4 ones. In powders, particles are in contact leading to an interparticle exchange which is not present in the dilute solutions where exchange bias properties are only due to an intraparticle exchange between core and surface. The thermal dependence of the bias field is well described by a reduced exponential behavior with a characteristic freezing temperature of about 8 K.