tSNE often offers better visual representation (separation) on such complicated data than PCA. As Micheal pointed out, computing a tSNE embedding over 20.000 gene dimensions is computationally unfeasible, so a number of PCs are normally calculated and these are used as input for calculating the tSNE. They are used in tandem.
As for global vs. local, we are much more interested to see similarity of cells to a limited number of neighbours indicating a celltype and grouping these close together. This is more important than the distance between such celltypes. (assuming the separation in your tSNE is driven by a biologically meaningful factor such as celltype and not some confounder)
Since I just made these images for myself anyway I might as well post them. The first 2 PCs show some separation by celltype, tSNE computed over 100 PCs gets very nice separation.