The structure and properties of vacancy loops (VIs) and stacking-fault tetrahedra (SFTs) in copper have been studied by computer simulation using a long-range pair interatomic potential (LRPP), obtained from the generalized pseudopotential theory, and a many-body potential (MBP) of Finnis-Sinclair type. The results obtained for these different potentials are qualitatively different. Thus, for the LRPP, significant atomic relaxation is observed for all defects. Triangular vacancy platelets relax into regular SFTs, and small hexagonal clusters form Frank loops, whereas large hexagonal clusters (containing more than 37 vacancies) can dissociate into six truncated SFTs with the side equal to the  side of the hexagon. Similar features are observed after the relaxation of circular loops. For the MBP, on the other hand, none of the hexagonal, circular and triangular planar vacancy platelets relax into a VL or SFT but remain almost unrelaxed 'holes', with a relative stability which is weakly dependent on the shape. The results obtained are compared with experiment and the results of other computer simulations, and the differences stemming from the use of different interatomic potentials and different simulation methods are discussed.