Gravitational lensing is a crucial tool for exploring cosmic phenomena, providing insights into galaxy clustering, dark matter, and dark energy. Given the substantial computational demands of N-body simulations, approximate methods like 𝙿𝙸𝙽𝙾𝙲𝙲𝙷𝙸𝙾 and 𝚝𝚞𝚛𝚋𝚘𝙶𝙻 have been proposed as viable alternatives for simulating lensing probability density functions (PDFs). This paper evaluates these methods and their effectiveness across both weak and strong lensing regimes, with a focus in the context where baryonic effects are negligible. Our comparative analysis reveals that these methods are effective for applications where lensing is mild, such as the majority of sources of electromagnetic and gravitational waves. However, both 𝙿𝙸𝙽𝙾𝙲𝙲𝙷𝙸𝙾 and 𝚝𝚞𝚛𝚋𝚘𝙶𝙻 break down for large values of convergence and magnification due to their loss of accuracy in capturing small-scale nonlinear matter fields, owing to oversimplified assumptions about internal halo structures and reliance on perturbation theory. 𝙿𝙸𝙽𝙾𝙲𝙲𝙷𝙸𝙾 yields second-to-fourth moments of the lensing PDFs, which are 6–10% smaller than those resulting from N-body simulations in regimes where baryonic effects are minimal. These findings aim to inform future studies on gravitational lensing of point sources, which are increasingly relevant with upcoming supernova and gravitational wave datasets.