The momentum equations that describe sea ice drift for aviscous-plastic (VP) ice rheology are difficult to solve numerically,because the associated bulk and shear viscosities can be verylarge. Traditionally, implicit solution techniques for the VP rheologyare thought to be expensive; the explicit elastic-viscous-plastic(EVP) method was designed to be more efficient and accurate. In orderto assess their relative performance, experiments with idealizedgeometry are used to compare model solutions of implicit VP- andexplicit EVP-solvers in two very different ice-ocean codes: theregular-grid, finite-volume Massachusetts Institute of Technologygeneral circulation model (MITgcm) and the Alfred Wegener InstituteFinite Element Ocean Model (FEOM). For both codes the obtainedsolutions of implicit VP- and EVP-solvers can differ significantly,because the EVP solutions tend to have smaller ice viscosities(weaker ice). EVP solutions tend to converge to implicit VPsolutions for very small sub-cycling time steps. A limiting scheme forEVP viscosities, that addresses a noise problem, reduces the viscosityeven further and, especially in the case of the variable-resolutionunstructured grids of FEOM, can lead to unexpected ice distributionsthat are dramatically different from solutions without thisscheme. Implicit VP-solvers are found to be generally faster than theEVP-solvers, most likely because the ice distribution does not changemuch within the short time steps of this study. Short time steps arethought to be typical of present day high resolution ice-ocean models,so that previous timing results for long time steps may no longer berepresentative.