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Tsunamis are rare events involving several complex physical phenomena. Due to this complexity and the relative scarcity of observations, tsunami research makes extensive use of numerical simulations. For seismogenic tsunamis, the source is often modeled as an instantaneous sea‐floor displacement (IS), while the tsunami propagation and inundation is computed through a shallow water approximation (SW). Here, we investigate what is the best tsunami inundation modeling strategy for different realistic earthquake source size and duration. We use 1D earthquake‐tsunami coupled simulations of large M> 8 earthquakes in Tohoku‐like subduction zone to test for which conditions the IS and/or the SW approximations can simulate with enough accuracy the tsunami evolution. We use as a reference a time‐dependent (TD), multi‐layer, non‐hydrostatic (NH) 1D model. Source duration, and size, are based on 1D dynamic rupture simulations with realistic stress drop and rigidity. We show that slow ruptures, generating slip in the shallow part of subduction zones (e.g., tsunami earthquakes), and very large events, with an along‐dip extent comparable with the trench‐coast distance (as occurs for megathrust events) require a TD‐NH modeling, especially for regions with steep coastal bathymetry. Conversely, deeper, higher stress‐drop events can be modeled through an IS‐SW approximation. We finally show that: (a) steeper bathymetries generate larger runups and, (b) a resonant mechanism emerges with runup amplifications associated with larger source size on flatter bathymetries. These results, obtained with 1D modeling, can serve as a guide for the appropriate 2/3D simulation approach for applications ranging from fundamental tsunami science to computational‐intensive hazard assessments. In the last two decades, tsunamis originated by large earthquakes have generated major damage and, according to the World Health Organization, more than 250 k casualties (more than 200 k due to the 2004 Indian Ocean tsunami). Strategies to quantify and mitigate the associated risk are based on numerical simulations of the physical processes regulating the generation, propagation of the waves and subsequent flooding on the coast. These simulations require significant computational resources. To make simulations more affordable, numerous approximations are introduced that need to be tested. In this work, we studied which earthquakes, depending on the speed at which they deform the sea bottom when they trigger a tsunami, and on how big they are, require a more detailed modeling approach, and which ones, instead, might be accurately simulated through approximated approaches. We also show how such findings are related to different bathymetric characteristics near the coast and inland, which may enhance or reduce the tsunami effects. Slow and large ruptures (e.g., tsunami earthquakes and megathrust) require a time‐dependent, non‐hydrostatic modelingDeeper, high stress‐drop earthquakes might be modeled through an instantaneous source, shallow water approximationInundation depends on bathymetric features: larger inundations on steeper depth gradients and resonant runup amplifications are observed Slow and large ruptures (e.g., tsunami earthquakes and megathrust) require a time‐dependent, non‐hydrostatic modeling Deeper, high stress‐drop earthquakes might be modeled through an instantaneous source, shallow water approximation Inundation depends on bathymetric features: larger inundations on steeper depth gradients and resonant runup amplifications are observed