Determining the key features of high-efficiency photosynthetic energy transfer remains an ongoing task. Recently, there has been evidence for the role of vibronic coherence in linking donor and acceptor states to redistribute oscillator strength for enhanced energy transfer. To gain further insights into the interplay between vibronic wavepackets and energy-transfer dynamics, we systematically compare four structurally related phycobiliproteins from cryptophyte algae by broad-band pump-probe spectroscopy and extend a parametric model based on global analysis to include vibrational wavepacket characterization. The four phycobiliproteins isolated from cryptophyte algae are two "open" structures and two "closed" structures. The closed structures exhibit strong exciton coupling in the central dimer. The dominant energy-transfer pathway occurs on the subpicosecond timescale across the largest energy gap in each of the proteins, from central to peripheral chromophores. All proteins exhibit a strong 1585 cm-1 coherent oscillation whose relative amplitude, a measure of vibronic intensity borrowing from resonance between donor and acceptor states, scales with both energy-transfer rates and damping rates. Central exciton splitting may aid in bringing the vibronically linked donor and acceptor states into better resonance resulting in the observed doubled rate in the closed structures. Several excited-state vibrational wavepackets persist on timescales relevant to energy transfer, highlighting the importance of further investigation of the interplay between electronic coupling and nuclear degrees of freedom in studies on high-efficiency photosynthesis.