Background: The formation of superheavy nuclei in fusion reactions is suppressed by a competing quasifission process. The competition between the formation of the compound nucleus and the quasifission depends strongly on the reaction entrance channel. Purpose: The investigation of fission and quasifission processes in the formation of Z=120 superheavy composite systems in the 52,54Cr+248Cm and 68Zn+232Th reactions, and their comparison with the 64Ni+238U reaction at energies in the vicinity of the Coulomb barrier. Methods: Mass-energy distributions of fissionlike fragments formed in the reactions 52,54Cr+248Cm and 68Zn+232Th at energies near the Coulomb barrier were measured using the double-arm time-of-flight spectrometer CORSET. Results: Capture cross sections for the reactions under investigation were measured. The most probable fragment masses and total kinetic energies as well as their variances in dependence on the interaction energy were studied for asymmetric and symmetric fragments. The fusion probabilities were estimated from the analysis of mass-energy distributions. Conclusions: The estimated fusion probability drops down by a factor of 103 in the 54Cr+248Cm reaction compared to the reactions of 48Ca ions with actinides. Among the studied reactions, the 54Cr+248Cm is the most favorable one for the production of the superheavy element with Z=120.