We study the dynamics of counterflowing bosonic and fermionic lithium atoms. First, by tuning the interaction strength we measure the critical velocity v(c) of the system in the BEC-BCS crossover in the low temperature regime and we compare it to the recent prediction of Castin et al., C. R. Phys. 16, 241 (2015). Second, raising the temperature of the mixture slightly above the superfluid transitions reveals an unexpected phase locking of the oscillations of the clouds induced by dissipation.