There are trade-offs between computational speed, accuracy, and constraints. The Eigen library has a pretty good summary here https://eigen.tuxfamily.org/dox/group__TopicLinearAlgebraDecompositions.html
(And there's also a page comparing SVD and QR-decomposition for least-square solvers at https://eigen.tuxfamily.org/dox/group__LeastSquares.html )
From this second page:
"The three methods discussed on this page are the SVD decomposition, the QR decomposition and normal equations. Of these, the SVD decomposition is generally the most accurate but the slowest, normal equations is the fastest but least accurate, and the QR decomposition is in between."