$ Weakgravitationallensingisapowerfulprobewhichisusedtoconstrainthestandardcosmologicalmodelanditsextensions.Withtheenhancedstatisticalprecisionofcurrentandupcomingsurveys,highaccuracypredictionsforweaklensingstatisticsareneededtolimittheimpactoftheoreticaluncertaintiesoncosmologicalparameterconstraints.Forthispurpose,wepresentacomparisonofthetheoreticalpredictionsforthenonlinearmatterandweaklensingpowerspectra,basedonthewidelyusedfittingfunctions(meadandrev-halofit),emulators(EuclidEmulator,EuclidEmulator2,BaccoEmulatorandCosmicEmulator)andN−bodysimulations(Pkdgrav3).WeconsidertheforecastedconstraintsontheΛCDMandwCDMmodelsfromweaklensingforstageIIIandstageIVsurveys.Westudytherelativebiasontheconstraintsandtheirdependenceontheassumedprescriptions.AssumingaΛCDMcosmology,wefindthattherelativeagreementontheS_8parameterisbetween0.2-0.3σforastageIII−likesurveybetweentheabovepredictors.ForastageIV−likesurveytheagreementbecomes1.4-3.0σ.InthewCDMscenario,wefindbroaderS_8constraints,andagreementsof0.18-0.26σand0.7-1.7σforstageIIIandstageIVsurveys,respectively.TheaccuraciesoftheabovepredictorsthereforeappearadequateforstageIIIsurveys,whilethefittingfunctionswouldneedimprovementsforfuturestageIVweaklensingsurveys.Furthermore,wefindthat,ofthefittingfunctions,mead$ provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of the future weak lensing surveys.