You are working with a genomic dataset containing 10,000 features and 5,000 samples. Compare and contrast the mathematical mechanisms of UMAP (Uniform Manifold Approximation and Projection) and t-SNE (t-Distributed Stochastic Neighbor Embedding) for reducing this data to 2 dimensions. Specifically, address how each algorithm handles the 'crowding problem' and preserves global versus local structure. Provide a recommendation for which algorithm to use if the goal is to identify distinct cellular subtypes.