Ternary mixtures of saturated and unsaturated phospholipids and cholesterol constitute a well-known model system to study raft formation in membranes. This phenomenon is, e.g., observed in cell membranes. Here, coarse-grained (CG) and microscopic united-atom (UA) simulations are performed to investigate the phase separation of a membrane bilayer for the ternary system of saturated 16:0 (DPPC) and unsaturated 18:2 (DUPC) phospholipids and cholesterol (CHOL). The results of a 9 mu s UA simulation demonstrate the onset of phase separation and can be compared with properties of the corresponding CG system. While sharing the structural features of phase separation in the CG model, the onset of demixing for the UA model is 40 times slower. This factor can be rationalized by the different short-time diffusion constants. Various system properties such as order parameters and lipid CHOL and CHOL CHOL interactions are analyzed and compared between the UA and CG models. From the structural perspective, the phase separation process appears to be rather similar for both models, which illustrates once more the power of using CG approaches.