Inelastic neutron scattering was used to probe the nature of the boson peak in atactic polypropylene (aPP), head-to-head polypropylene (hhPP), polyisobutylene (PIB) and a 1/1 mass ratio hhPP/PIB blend. Atactic polypropylene is among the most "fragile" of glass formers and was found to have a shoulder rather than the distinctive peak exhibited by the other three polymers. This difference is already apparent at 15 K where relaxations are not expected to occur. The results suggest that the fragility of hhPP is intermediate between aPP and PIB. Within this group of polymers which have similar chemical structures the position of the boson peak appears to correlate with the glass transition temperature and the cohesive energy density. The possibility of a correlation with chain stiffness as expressed by the characteristic ratio is also discussed.