Fine-tuning large language models (LLMs) for machine translation has shown improvements in overall translation quality. However, it is unclear what is the impact of fine-tuning on desirable LLM behaviors that are not present in neural machine translation models, such as steerability, inherent document-level translation abilities, and the ability to produce less literal translations. We perform an extensive translation evaluation on the LLaMA and Falcon family of models with model size ranging from 7 billion up to 65 billion parameters. Our results show that while fine-tuning improves the general translation quality of LLMs, several abilities degrade. In particular, we observe a decline in the ability to perform formality steering, to produce technical translations through few-shot examples, and to perform document-level translation. On the other hand, we observe that the model produces less literal translations after fine-tuning on parallel data. We show that by including monolingual data as part of the fine-tuning data we can maintain the abilities while simultaneously enhancing overall translation quality. Our findings emphasize the need for fine-tuning strategies that preserve the benefits of LLMs for machine translation.