For once Cholesky is less general than QR: Cholesky only makes sense for positive matrices, while QR works for any matrix (including non square). Also QR is a

For once Cholesky is less general than QR: Cholesky only makes sense for positive matrices, while QR works for any matrix (including non square). Also QR is a primitive for operations like finding eigenvalues, and I don't think Cholesky can be used there.