Despite major recent efforts, marine ice sheet models aiming at predicting future mass loss from ice sheets still suffer from uncertainties with respect to grounding line migration. A recent model intercomparison provided tools to test how models treat grounding line dynamics in a three-dimensional setting. Here we use these tools to address to what extent differences in mass loss occur according to the approximation to the Stokes equations, describing marine ice sheet flow, used. We find that models that neglect components of vertical shearing in the force budget wrongly estimate ice sheet mass loss by ±50% over century time scales when compared to models that solve the full Stokes system of equations. Models that only include horizontal stresses also misrepresent velocities and ice shelf geometry, suggesting that interactions between the grounded ice sheet and the ocean will also be modeled incorrectly. Based on these findings, we strongly advise the use of high-order models to compute reliable projections of ice sheet contribution to sea level rise.