Biological vision systems make adaptive use of context to recognize objects in new settings with novel contexts as well as occluded or blurry objects in familiar settings. In this paper, we investigate how vision models adaptively use context for out-of-distribution (OOD) generalization and leverage our analysis results to improve model OOD generalization. First, we formulate two distinct OOD settings where the contexts are either beneficial Object-Disambiguation or irrelevant Background-Invariance, reflecting the diverse contextual challenges faced in biological vision. We then analyze model performance in these two different OOD settings and demonstrate that models that excel in one setting tend to struggle in the other. Notably, prior works on learning causal features improve on one setting but hurt on the other. This underscores the importance of generalizing across both OOD settings, as this ability is crucial for both human cognition and robust AI systems. Next, to better understand the model properties contributing to OOD generalization, we use representational geometry analysis and our own probing methods to examine a population of models, and we discover that those with more factorized representations and appropriate feature weighting are more successful in handling Object-Disambiguation and Background-Invariance tests. We further validate these findings through causal intervention, manipulating representation factorization and feature weighting to demonstrate their causal effect on performance. Motivated by our analysis results, we propose new augmentation methods aimed at enhancing model generalization. The proposed methods outperform strong baselines, yielding improvements in both in-distribution and OOD tests. We conclude that, in order to replicate the generalization abilities of biological vision, computer vision models must have factorized object vs. background representations and appropriately weigh both kinds of features.