In this paper, the suspension core-tube structure and frame core-tube structure are taken as the research objects, and the modal analysis of them and their basic seismic isolation structures are carried out firstly to explore the self-vibration characteristics and seismic isolation effect of the structures. Secondly, the nonlinear time-history analysis of the four structures under the action of rare earthquakes in the X, Y, and Z directions is carried out, and their inter-story drift angles, inter-story shear forces, base shear forces, maximum accelerations at the apex of the core-tube, and cantilever beam stresses are analyzed comparatively. Finally, the displacements and loads of the energy dissipators, the maximum horizontal displacements and tensile and compressive stresses of the seismic isolation bearings are analyzed to evaluate the performance of both of them under rare earthquakes. The results show that the suspension core-tube structure and the frame core-tube structure with base seismic isolation bearings can provide good control of their inter-story drift angles and internal forces, etc. The suspension core-tube structure is superior to the frame core-tube structure in controlling the maximum acceleration at the apex of the core tube response.