We compare the efficiency of moments and Minkowski functionals (MFs) in constraining the subset of cosmological parameters (Omega_m,w,sigma_8) using simulated weak lensing convergence maps. We study an analytic perturbative expansion of the MFs in terms of the moments of the convergence field and of its spatial derivatives. We show that this perturbation series breaks down on smoothing scales below 5, while it shows a good degree of convergence on larger scales (15). Most of the cosmological distinguishing power is lost when the maps are smoothed on these larger scales. We also show that, on scales comparable to 1, where the perturbation series does not converge, cosmological constraints obtained from the MFs are approximately 1.5-2 times better than the ones obtained from the first few moments of the convergence distribution --- provided that the latter include spatial information, either from moments of gradients, or by combining multiple smoothing scales. Including either a set of these moments or the MFs can significantly tighten constraints on cosmological parameters, compared to the conventional method of using the power spectrum alone.
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