In this study, we focus on qualitative differences in the network structure and dynamics of natural as well as poly(butadiene) rubber in dependence of the cure system (sulfur/accelerator or organic peroxide) used in the vulcanization process. The spatial homogeneity of the distribution of chemical and physical cross-links in the network is assessed via the quantitative measurement of proton-proton residual dipolar couplings as measured by static multiple-quantum (MQ) NMR spectroscopy at low field. The experiment also provides information on the apparent correlation time of fast segmental fluctuations that dominate chain relaxation processes at lower temperature, for which we also find characteristic differences. Vulcanization via a radical mechanism (using organic peroxides) leads to networks with a high content of nonelastic defects (loops or dangling chains), a rather inhomogeneous distribution of cross-links, and modified (slower) local dynamics, as compared to networks obtained by sulfur vulcanization. These microstructural factors can be related with the well-known differences in the macroscopic properties of diene rubbers vulcanized with different cure systems.