The behaviors of three different catalyst systems, TiCl4/MgCl2, Cp2ZrCl2 and Cp2HfCl2, were investigated in ethylene/1,5‐hexadiene copolymerization. In the Fourier transform infrared spectra of the copolymers, cyclization and branching were detected for 1,5‐hexadiene insertion in the metallocene and Ziegler–Natta systems, respectively. DSC and viscometry analyses results revealed that copolymers with lower Tm and crystallinity and higher molecular weight were obtained with metallocene catalysts. The sequence length distribution of the copolymers was investigated by using the successive self‐nucleation and annealing thermal fractionation technique. The continuous melting endotherms obtained from successive self‐nucleation and annealing analysis were employed to get information about short‐chain branching, the branching dispersity index, comonomer content and lamella thickness in the synthesized copolymers. The results established that metallocene catalysts were much more effective than Ziegler–Natta catalysts in the incorporation of 1,5‐hexadiene in the polyethylene structure. Metallocene‐based copolymers had higher short‐chain branching and comonomer content, narrower branching dispersity index and thinner lamellae. Finally, the tendency of the employed catalysts in the 1,5‐hexadiene incorporation and cyclization reaction was explored via molecular simulation. The energy results demonstrated that, in comparison to Ziegler–Natta, metallocene catalysts have a much higher tendency to 1,5‐hexadiene incorporation and cyclization. © 2018 Society of Chemical Industry