Foundations models are presented as generalists that often perform well over a myriad of tasks. Fine-tuning these models, even on limited data, provides an additional boost in task-specific performance but often at the cost of their wider generalization, an effect termed catastrophic forgetting. In this paper, we analyze the relation between task difficulty in the CLIP model and the performance of several simple parameter-efficient fine-tuning methods through the lens of domain generalization and catastrophic forgetting. We provide evidence that the silhouette score of the zero-shot image and text embeddings is a better measure of task difficulty than the average cosine similarity of correct image/label embeddings, and discuss observable relationships between task difficulty, fine-tuning method, domain generalization, and catastrophic forgetting. Additionally, the averaged results across tasks and performance measures demonstrate that a simplified method that trains only a subset of attention weights, which we call A-CLIP, yields a balance between domain generalization and catastrophic forgetting.