fMRI data is inherently high-dimensional and difficult to visualize. A recent trend has been to find spaces of lower dimensionality where functional brain networks can be projected onto manifolds as individual data points, leading to new ways to analyze and interpret the data. Here, we investigate the potential of two powerful non-linear manifold learning techniques for functional brain networks representation: (1) T-stochastic neighbor embedding (t-SNE) and (2) Uniform Manifold Approximation Projection (UMAP) a recent breakthrough in manifold learning. fMRI data from the Human Connectome Project (HCP) and an independent study of aging were used to generate functional brain networks. We used fMRI data collected during resting state data and during a working memory task. The relative performance of t-SNE and UMAP were investigated by projecting the networks from each study onto 2D manifolds. The levels of discrimination between different tasks and the preservation of the topology were evaluated using different metrics. Both methods effectively discriminated the resting state from the memory task in the embedding space. UMAP discriminated with a higher classification accuracy. However, t-SNE appeared to better preserve the topology of the high-dimensional space. When networks from the HCP and aging studies were combined, the resting state and memory networks in general aligned correctly. Our results suggest that UMAP, a more recent development in manifold learning, is an excellent tool to visualize functional brain networks. Despite dramatic differences in data collection and protocols, networks from different studies aligned correctly in the embedding space.