Despite the significant potential of Foundation Models (FMs) in medical imaging, their application to prognosis prediction remains challenging due to data scarcity, class imbalance, and task complexity, which limit their clinical adoption. This study introduces the first structured benchmark to assess the robustness and efficiency of transfer learning strategies for FMs compared with convolutional neural networks (CNNs) in predicting COVID-19 patient outcomes from chest X-rays. The goal is to systematically compare finetuning strategies, both classical and parameter efficient, under realistic clinical constraints related to data scarcity and class imbalance, offering empirical guidance for AI deployment in clinical workflows. Four publicly available COVID-19 chest X-ray datasets were used, covering mortality, severity, and ICU admission, with varying sample sizes and class imbalances. CNNs pretrained on ImageNet and FMs pretrained on general or biomedical datasets were adapted using full finetuning, linear probing, and parameter-efficient methods. Models were evaluated under full data and few shot regimes using the Matthews Correlation Coefficient (MCC) and Precision Recall AUC (PR-AUC), with cross validation and class weighted losses. CNNs with full fine-tuning performed robustly on small, imbalanced datasets, while FMs with Parameter-Efficient Fine-Tuning (PEFT), particularly LoRA and BitFit, achieved competitive results on larger datasets. Severe class imbalance degraded PEFT performance, whereas balanced data mitigated this effect. In few-shot settings, FMs showed limited generalization, with linear probing yielding the most stable results. No single fine-tuning strategy proved universally optimal: CNNs remain dependable for low-resource scenarios, whereas FMs benefit from parameter-efficient methods when data are sufficient.