This study assesses whether self-supervised learning (SSL) improves knee osteoarthritis (OA) modeling for diagnosis and prognosis relative to ImageNet-pretrained initialization. We compared (i) image-only SSL pretrained on knee radiographs from the OAI, MOST, and NYU cohorts, and (ii) multimodal image-text SSL pretrained on hospital knee radiographs paired with radiologist impressions. For diagnostic Kellgren-Lawrence (KL) grade prediction, SSL yielded mixed results. While image-only SSL improved accuracy during linear probing (frozen encoder), it did not outperform ImageNet pretraining during full fine-tuning. Similarly, multimodal SSL failed to improve grading performance. A likely explanation is mismatch between the hospital pretraining corpus and the downstream diagnostic task: the hospital image-text dataset was restricted to knees from patients with clinically identified OA in routine care, rather than a cohort spanning the full spectrum from normal to severe disease needed for balanced KL grading. In addition, radiology impressions do not explicitly encode KL grade, limiting supervision for learning KL-specific decision boundaries. In contrast, this same multimodal initialization significantly improved prognostic modeling. It outperformed ImageNet baselines in predicting 4-year structural incidence and progression, including on external validation (MOST AUROC: 0.701 vs. 0.599 at 10\% labeled data). Overall, these results suggest that our hospital image-text data may be less effective for diagnostic grading when the pretraining cohort is limited to OA knees, but can provide a strong signal for prognostic modeling when the downstream task is better aligned with the pretraining data distribution.