A reliable structural analysis of monumental masonry domes depends on several factors, including accurate geometry and the constitutive law of the material. However, an excessively refined material model can pose challenges in parameter identification and result in high computational costs. This paper addresses two main objectives. First, it compares the results obtained using the commercial FE program Abaqus on a dome with idealized geometry to those based on the exact geometry, derived from an accurate laser scanning survey. Second, it compares the FE results, using a sophisticated nonlinear material model, the Concrete Damage Plasticity model available in Abaqus, with those obtained from Thrust Network Analysis (TNA): this approach, able to incorporate the simple yet effective no-tension assumption for masonry vaults, was recently re-formulated within multi-constrained optimization problems. The dome of the Cathedral of Pisa, Italy, subjected to gravity loads serves as the case study. The numerical outcomes indicate that neglecting imperfections in real domes can lead to inaccurate results when using oversimplified, idealized geometries. Additionally, the TNA proves to be a powerful numerical method, providing results as accurate as the FEM, but without the uncertainties associated with defining the mechanical behavior of masonry.