Mechanical and dielectric spectroscopy studies of local segmental motion (alpha-relaxation) in polybutadienes are reviewed and new results presented. Previous mechanical spectra for 1,4-polybutadiene relied on time-temperature superpositioning, leading to discrepancies regarding the breadth of the relaxation function. By measuring over a wide range of actual frequencies, we show that the mechanical dispersion is narrow, relative to 1,2-polybutadiene. The disagreement among published dielectric alpha-relaxation results is shown to be a consequence of the intrusion of the secondary relaxation for temperatures near the glass transition. The actual breadth of the relaxation function can be gleaned from analysis of the temperature dependence of the alpha-relaxation time and is consistent with the determination from mechanical spectroscopy (i.e., a narrow dispersion). Thus, decreasing vinyl content is associated with a narrower segmental relaxation function, whereby the correlation of chemical structure with both the breadth of the relaxation function and its temperature dependence holds for polybutadiene. This is in accord with an interpretation of the segmental dynamics based on steric interactions involving the pendant vinyl group enhancing intermolecular cooperativity. The T-g-normalized temperature dependences for 1,2- and 1,4-polybutadiene are also consistent with the respective energy barriers between conformational states of their backbones.