Multi-omic analyses are necessary to understand the complex biological processes taking place at the tissue and cell level, but also to make reliable predictions about, for example, disease outcome. Several linear methods exist that create a joint embedding using paired information per sample, but recently there has been a rise in the popularity of neural architectures that embed paired -omics into the same non-linear manifold. This work describes a head-to-head comparison of linear and non-linear joint embedding methods using both bulk and single-cell multi-modal datasets. We found that non-linear methods have a clear advantage with respect to linear ones for missing modality imputation. Performance comparisons in the downstream tasks of survival analysis for bulk tumor data and cell type classification for single-cell data lead to the following insights: First, concatenating the principal components of each modality is a competitive baseline and hard to beat if all modalities are available at test time. However, if we only have one modality available at test time, training a predictive model on the joint space of that modality can lead to performance improvements with respect to just using the unimodal principal components. Second, -omic profiles imputed by neural joint embedding methods are realistic enough to be used by a classifier trained on real data with limited performance drops. Taken together, our comparisons give hints to which joint embedding to use for which downstream task. Overall, product-of-experts performed well in most tasks and was reasonably fast, while early integration (concatenation) of modalities did quite poorly.