Linear residualization is a common practice for confounding adjustment in machine learning applications. Recently, causality-aware predictive modeling has been proposed as an alternative causality-inspired approach for adjusting for confounders. In this paper, we compare the linear residualization approach against the causality-aware confounding adjustment in anticausal prediction tasks. Our comparisons include both the settings where the training and test sets come from the same distributions, as well as, when the training and test sets are shifted due to selection biases. In the absence of dataset shifts, we show that the causality-aware approach tends to (asymptotically) outperform the residualization adjustment in terms of predictive performance in linear learners. Importantly, our results still holds even when the true model generating the data is not linear. We illustrate our results in both regression and classification tasks. Furthermore, in the presence of dataset shifts in the joint distribution of the confounders and outcome variables, we show that the causality-aware approach is more stable than linear residualization.