Two fundamentally different types of dual-frequency (DF) capacitively coupled radio frequency discharges can be used for plasma processing applications to realize separate control of the ion mean energy, < E-i >, and the ion flux, Gamma(i), at the substrate surface: (i) classical discharges operated at substantially different frequencies, where the low-and high-frequency voltage amplitudes, phi(lf) and phi(hf), are used to control < E-i > and Gamma(i), respectively; (ii) electrically asymmetric (EA) discharges operated at a fundamental frequency and its second harmonic with fixed, but adjustable phase shift between the driving frequencies, theta. In EA discharges the voltage amplitudes are used to control Gamma(i) and theta is used to control < E-i >. Here, we report our systematic simulation studies of the effect of secondary electrons on the ionization dynamics and the quality of this separate control in both discharge types in argon at different gas pressures. We focus on the effect of the control parameter for < E-i > on Gamma(i) for different secondary yields, gamma. We find a dramatic effect of tuning phi(lf) in classical DF discharges, which is caused by a transition from alpha-to. gamma-mode induced by changing phi(lf). In EA discharges we find that no such mode transition is induced by changing theta within the parameter range studied here and, consequently, Gamma(i) remains nearly constant as a function of theta. Thus, despite some limitations at high values of. the quality of the separate control of ion energy and flux is generally better in EA discharges compared with classical DF discharges.