We study the effect of chemical composition in copolymers of ethylene and higher α-olefins, butene-1 (PEB), hexene-1 (PEH), octene-1 (PEO) and decene-1 (PED) on the structural, conformational and thermodynamic properties of their melts. To this end, we perform extensive simulations using a connectivity altering Monte Carlo method extended to short chain branched copolymers. Good equilibration of the systems considered (melts of long chains containing on average 1000 carbon atoms in the backbone and up to 20-40 mol% of α-olefin) has been achieved. The calculated values of radii of gyration, <S2>, plotted against the weight fraction of side chains, fb, fall approximately on a single curve, in agreement with experiment based correlations. The observed reduction of chain dimensions is due to an increase in the population of gauche conformational states along the backbones. Other properties, such as cohesive energies and primitive paths from topological analyses of melts also form common curves when plotted with respect to fb. Molecular mechanisms underlying the observed evolution in structural and thermodynamic properties will be discussed.