I know how to calculate PCA and SVD mathematically, and I know that both can be applied to Linear Least Squares regression.
The main advantage of SVD mathematically seems to be that it can be applied to non-square matrices.
Both focus on the decomposition of the $X^\top X$ matrix. Other than the advantage of SVD mentioned, are there any additional advantages or insights provided by using SVD over PCA?
I'm really looking for the intuition rather than any mathematical differences.