Derivative-free optimization can be used to estimate parameters without computing derivatives. As there exist many methods, it is unclear which to use in practice. Here, we present two comparative studies of 18 state-of-the-art methods: Firstly, we evaluate them on a set of 466 classic optimization test problems of dimension 2 to 300. Secondly, we study their performance in parameter estimation on 8 ODE models of biological processes, comparing them to state-of-the-art derivative-based optimization. We observe that different problem features necessitate the use of different methods, for which we can give suggestions based on our findings. Our analysis suggests that classic test problems are not representative for problems in systems biology. For ODE models, we find that purely derivative-free methods are for most problems not reliable or at least inferior to derivative-based methods.