The use of deep generative models for unsupervised anomaly detection is an area of research that has gained interest in recent years in the field of medical imaging. Among all the existing models, the variational autoencoder (VAE) has proven to be efficient while remaining simple to use. Much research to improve the original method has been achieved in the computer vision literature, but rarely translated to medical imaging applications. To fill this gap, we propose a benchmark of fifteen variants of VAE that we compare with a vanilla autoencoder and VAE for a neuroimaging use case relying on a simulation-based evaluation framework. The use case is the detection of anomalies related to Alzheimer's disease and other dementias in 3D FDG PET. We show that among the fifteen VAE variants tested, nine lead to a good reconstruction accuracy and are able to generate healthy-looking images. This indicates that many approaches developed for computer vision applications can generalize to the unsupervised detection of anomalies of various shapes, intensities and locations in 3D FDG PET. However, these models do not outperform the vanilla autoencoder and VAE.