I think this is largely because how the clusters are distributed in sample space. For instance, in cancer research we usually have overlapping Gaussian clusters. Often quite a simple structure. Both PCA and tSNE work fine to show these structures in my experience. Sometimes, but rarely, the structures in some datasets may be more complex, towards single cell RNA-seq complexity, and tSNE works better in these situations.
In single cell RNA-seq oftentimes we have far more complex structures usually consisting of many globular clusters (cell types) of different sizes and variance arranged in complex patterns in sample space. tSNE can capture complex non-linear structures well, PCA can't.
Edit: you may want to look into the UMAP algorithm.