Dynamic mechanical analysis was used to study ethylene/1-hexene copolymers with different compositions, molecular weight distributions, and profiles of short-chain branching (SCB) versus molecular weight. These copolymers were produced over a highly active supported titanium–magnesium catalyst (TMC), a highly active supported vanadium–magnesium catalysts (VMC), and a supported zirconocene catalyst. A higher fraction of the crystalline phase in the copolymers prepared with VMC was shown to result in higher elastic modulus values. β relaxation was found to be sensitive to the SCB distribution versus the molecular weight. The copolymers prepared with the zirconocene catalyst and VMC were characterized by more uniform SCB distributions and higher temperatures of β relaxation compared to the copolymers prepared with TMC. The mobility of the polymer chains at room temperature in the amorphous phase obtained by the spin-probe method rose with increasing branch content in the copolymers and was not sensitive to different SCB distribution profiles.