PCA is a linear dimensionality reduction technique designed to model the variability based on the global structure of the data, while T-SNE is a non-linear technique that is optimal for capturing the local structure of high-dimensional data.
T-SNE is better suited to handle outliers, as where PCA would project outliers onto the axis that captures the largest proportion of overall variability, T-SNE is more likely to partition outliers into a different neighborhood than regions of higher density.
T-SNE is considered a more modern technique that generally is preferred over PCA, especially for data exploration and visualization. It does require tuning hyper-parameters such as perplexity and learning rate, whereas PCA requires little tuning besides choosing the number of components post-hoc.
