C-13 and Si-29 spin-lattice relaxation in nitrogen-doped 6H-polytype silicon carbide is highly site-dependent. Not only do carbon sites relax much more rapidly than the corresponding silicon sites, but also there are unprecedented differences in relaxation efficiency among the different carbon, and among the different silicon, sites, that can be related to much higher unpaired electron density in the conduction band at the higher-symmetry (types A and B) sites than at the lowest-symmetry (type C) site. In contrast, all sites relax at equivalent rates in most other 6H silicon carbide samples, including both commercial abrasive grade material with high levels of impurities and high-purity aluminum-doped and undoped samples. The nature of the relaxation process differs as well, from stretched exponential in lower-purity to exponential in high-purity samples.