Ensembles of deep neural networks have achieved great success recently, but they do not offer a proper Bayesian justification. Moreover, while they allow for averaging of predictions over several hypotheses, they do not provide any guarantees for their diversity, leading to redundant solutions in function space. In contrast, particle-based inference methods, such as Stein variational gradient descent (SVGD), offer a Bayesian framework, but rely on the choice of a kernel to measure the similarity between ensemble members. In this work, we study different SVGD methods operating in the weight space, function space, and in a hybrid setting. We compare the SVGD approaches to other ensembling-based methods in terms of their theoretical properties and assess their empirical performance on synthetic and real-world tasks. We find that SVGD using functional and hybrid kernels can overcome the limitations of deep ensembles. It improves on functional diversity and uncertainty estimation and approaches the true Bayesian posterior more closely. Moreover, we show that using stochastic SVGD updates, as opposed to the standard deterministic ones, can further improve the performance.