The stationary parameterization of diffeomorphisms is be- ing increasingly used in computational anatomy. In certain applications it provides similar results to the non-stationary parameterization alle- viating the computational charge. With this characterization for diffeo- morphisms, two different registration algorithms have been recently pro- posed: stationary LDDMM and diffeomorphic Demons. To our knowl- edge, their theoretical and practical differences have not been analyzed yet. In this article we provide a comparison between both algorithms in a common framework. To this end, we have studied the differences in the elements of both registration scenarios. We have analyzed the sen- sitivity of the regularization parameters in the smoothness of the final transformations and compared the performance of the registration re- sults. Moreover, we have studied the potential of both algorithms for the computation of essential operations for further statistical analysis. We have found that both methods have comparable performance in terms of image matching although the transformations are qualitatively different in some cases. Diffeomorphic Demons shows a slight advantage in terms of computational time. However, it does not provide as stationary LD- DMM the vector field in the tangent space needed to compute statistics or exact inverse transformations.