Polar ice is known to be one of the most anisotropic natural materials. For a given fabric the polycrystal viscous response is strongly dependent on the actual state of stress and strain rate. Within an ice sheet, grounded-ice parts and ice shelves have completely different stress regimes, so one should expect completely different impacts of ice anisotropy on the flow. The aim of this work is to quantify, through the concept of enhancement factors, the influence of ice anisotropy on the flow of grounded ice and ice shelves. For this purpose, a full-Stokes anisotropic marine ice-sheet flowline model is used to compare isotropic and anisotropic diagnostic velocity fields on a fixed geometry. From these full-Stokes results, we propose a definition of enhancement factors for grounded ice and ice shelves, coherent with the asymptotic models used for these regions. We then estimate realistic values for the enhancement factors induced by ice anisotropy for grounded ice and ice shelves.