  We investigate the potential of weak gravitational lensing maps to
differentiate between distinct cosmological models, considering cosmic variance
due to a limited map extension and the presence of noise. We introduce a
measure of the differentiation between two models under a chosen lensing
statistics. That enables one to determine in which circumstances (map size and
noise level), and for which lensing measures two models can be differentiated
at a desired confidence level. As an application, we simulate convergence maps
for three cosmological models (SCDM, OCDM, and $\Lambda$CDM), calculate several
lensing analyses for them, and compute the differentiation between the models
under these analyses. We use first, second, and higher order statistics,
including Minkowski functionals, which provide a complete morphological
characterization of the lensing maps. We examine for each lensing measure used
how noise affects its description of the convergence, and how this affects its
ability to differentiate between cosmological models. Our results corroborate
to the valuable use of weak gravitational lensing as a cosmological tool.
