Numerical models are powerful tools to predict the electromagnetic behavior of superconductors. In recent years, a variety of models have been successfully developed to simulate high-temperature-superconducting (HTS) coated conductor tapes. While the models work well for the simulation of individual tapes or relatively small assemblies, their direct applicability to devices involving hundreds or thousands of tapes, as for example coils used in electrical machines, is questionable. Indeed the simulation time and memory requirement can quickly become prohibitive. In this article, we develop and compare two different models for simulating realistic HTS devices composed of a large number of tapes: 1) the homogenized model simulates the coil using an equivalent anisotropic homogeneous bulk with specifically developed current constraints to account for the fact that each turn carries the same current; 2) the multi-scale model parallelizes and reduces the computational problem by simulating only several individual tapes at significant positions of the coil's cross-section using appropriate boundary conditions to account for the field generated by the neighboring turns. Both methods are used to simulate a coil made of 2000 tapes, and compared against the widely used H-formulation finite element model that includes all the tapes. Both approaches allow speeding-up simulations of large number of HTS tapes by 1-3 orders of magnitudes, while keeping a good accuracy of the results. Such models could be used to design and optimize large-scale HTS devices.