The conformational fluctuations of proteins can be described using structural ensembles. To address the challenge of determining these ensembles accurately, a wide range of strategies have recently been proposed to combine molecular dynamics simulations with experimental data. Quite generally, there are two ways of implementing this type of approach, either by applying structural restraints during a simulation, or by reweighting a posteriori the conformations from an a priori ensemble. It is not yet clear, however, whether these two approaches can offer ensembles of equivalent quality. The advantages of the reweighting method are that it can involve any type of starting simulation and that it enables the integration of experimental data after the simulations are run. A disadvantage, however, is that this procedure may be inaccurate when the a priori ensemble is of poor quality. Here, our goal is to systematically compare the restraining and reweighting approaches and to explore the conditions required for the reweighted ensembles to be accurate. Our results indicate that the reweighting approach is computationally efficient and can perform as well as the restraining approach when the a priori sampling is already relatively accurate. More generally, to enable an effective use of the reweighting approach by avoiding the pitfalls of poor sampling, we suggest metrics for the quality control of the reweighted ensembles.