Both cerium (Ce) and praseodymium (Pr) undergo a volume collapse transition under compression that originate from similar electronic mechanisms. Yet the outcome could not be more different. In the case of Ce with one affected 4f electron the volume collapse leaves the crystal symmetry intact, whereas for Pr with two 4f electrons the crystal symmetry changes from a distorted face centered cubic structure to a lower symmetry orthorhombic structure. In this paper, we present a study of the effect of strain/compression rate spanning nearly 4 orders of magnitude on the volume collapse phase transitions in Ce and Pr. These dynamic compression experiments in a diamond anvil cell also reveal kinetic differences between the phase transformations observed in these two materials. The transition cannot be overdriven in pressure in Ce, which indicates a fast kinetic process, whereas fast compression rates in Pr lead to a shift of the phase boundary to higher pressures, pointing to slower kinetics possibly due to the realization of a new crystal structure.