Sparsification reduces the size of networks while preserving structural and statistical properties of interest. Various sparsifying algorithms have been proposed in different contexts. We contribute the first systematic conceptual and experimental comparison of \textit{edge sparsification} methods on a diverse set of network properties. It is shown that they can be understood as methods for rating edges by importance and then filtering globally or locally by these scores. We show that applying a local filtering technique improves the preservation of all kinds of properties. In addition, we propose a new sparsification method (\textit{Local Degree}) which preserves edges leading to local hub nodes. All methods are evaluated on a set of social networks from Facebook, Google+, Twitter and LiveJournal with respect to network properties including diameter, connected components, community structure, multiple node centrality measures and the behavior of epidemic simulations. In order to assess the preservation of the community structure, we also include experiments on synthetically generated networks with ground truth communities. Experiments with our implementations of the sparsification methods (included in the open-source network analysis tool suite NetworKit) show that many network properties can be preserved down to about 20\% of the original set of edges for sparse graphs with a reasonable density. The experimental results allow us to differentiate the behavior of different methods and show which method is suitable with respect to which property. While our Local Degree method is best for preserving connectivity and short distances, other newly introduced local variants are best for preserving the community structure.