This work studies the effects of rest time on the discharge response and the parameters of the Thevenin's equivalent circuit model for a li-ion battery. It is a continuation of our recent work on the effect of rest time on a lead-acid battery. While there are some similarities between the effects of rest time on the two batteries, significant differences are also revealed about the effects on initial conditions, time constants, resistances and capacitances. For the lead-acid battery, the relationships are mostly monotonic. For the li-ion battery, the relationships are more complex and demonstrate some oscillations before reaching a steady state.