Using molecular dynamics simulations we analyze the dynamics of two atomic liquids that display a liquid-liquid phase transition (LLPT): Si described by the Stillinger-Weber potential and Ga as modeled by the modified embedded-atom model. In particular, our objective is to investigate the extent to which the presence of a dip in the self-intermediate scattering function is a manifestation of an excess of vibrational states at low frequencies and may be associated with a fragile-to-strong transition (FTST) across the LLPT, as suggested recently. Our results suggest a somewhat different picture. First, in the case of Ga we observe the appearance of an excess of vibrational states at low frequencies, even in the absence of the appearance of a dip in the self-intermediate scattering function across the LLPT. Second, studying the behavior of the shear viscosities traversing the LLPTs we find that both substances are fragile in character above and below their respective LLPT temperatures. Instead of a FTST in an absolute sense these findings are more in line with a view in which the LLPTs are accompanied by a transition from a more fragile to a less fragile liquid. Furthermore, we do not find this transition to correlate with the presence of a dip in the intermediate scattering function.139224504