Is there any reason to think that SVD is better than PCA (by eigendecomposition) in decorrelating the predictors of a machine learning model?
To the best of my knowledge, the answer to your question is no. Regarding finding the correlations of different variables, they work the same. They both capture linear associations and do not capture nonlinear ones. The difference between them is mostly about numerical computation which makes SVD more handy than traditional PCA. I recommend having a look at this answer and this explanation.
As a final remark, let’s discuss the numerical advantages of using SVD. A basic approach to actually calculating PCA on a computer would be to perform the eigenvalue decomposition of $X^TX$ directly. It turns out that doing so would introduce some potentially serious numerical issues that could be avoided by using SVD.