This paper presents the first neutron scattering measurement of 1,2-1,4-polybutadienes with varying microstructure. Incoherent inelastic scattering experiments have been performed in the range of moderate (Delta E approximate to 300 mu eV) and high (Delta E approximate to 20 mu eV) energy resolution. For the moderate resolution experiments the vibration-relaxation model has been used as a guideline for interpretation. The most striking influence of the microstructure variation can be found in the position of the boson peak. Its position at low temperature as well as its temperature dependence is significantly different among the measured samples. The high resolution data have been Fourier transformed into the time domain yielding the intermediate incoherent scattering function in a time range of 5,...,150 ps. There, the basic properties found for 1,4-polybutadiene earlier could be reproduced (separation of alpha and beta(slow) regimes of the slow relaxation, Kohlrausch-Williams-Watts function with beta approximate to 0.4). On the basis of the new data, no microstructure induced differences can be detected except for the changes of temperature dependence due to the strongly different glass-transition temperatures and different fragility.