As the capabilities of pre-trained large language models (LLMs) continue to advance, the "pre-train and fine-tune" paradigm has become increasingly mainstream, leading to the development of various fine-tuning methods. However, the privacy risks arising from memorization during fine-tuning have received relatively little attention. To address this gap, we categorize popular fine-tuning approaches and assess their impact on memorization through the lens of membership inference attacks (MIAs). Our results show that, compared to parameter-based fine-tuning, prompt-based fine-tuning achieves competitive performance while exhibiting lower vulnerability to MIAs. Furthermore, prompt-based methods maintain low memorization regardless of model scale. These findings suggest that parameter-based fine-tuning is more prone to leaking private information, whereas prompt-based fine-tuning serves as a more privacy-preserving option.