The neural codec model reduces speech data transmission delay and serves as the foundational tokenizer for speech language models (speech LMs). Preserving emotional information in codecs is crucial for effective communication and context understanding. However, there is a lack of studies on emotion loss in existing codecs. This paper evaluates neural and legacy codecs using subjective and objective methods on emotion datasets like IEMOCAP. Our study identifies which codecs best preserve emotional information under various bitrate scenarios. We found that training codec models with both English and Chinese data had limited success in retaining emotional information in Chinese. Additionally, resynthesizing speech through these codecs degrades the performance of speech emotion recognition (SER), particularly for emotions like sadness, depression, fear, and disgust. Human listening tests confirmed these findings. This work guides future speech technology developments to ensure new codecs maintain the integrity of emotional information in speech.