Understanding how language is processed and represented cognitively increasingly involves the use of specialized language models. Yet, because most models are predominantly trained on written text, they struggle to reflect the characteristics of language as it naturally unfolds in spoken interaction. This gap limits their capabilities in capturing features typical of spontaneous speech, such as repetitions, feedback cues, and hesitations. In this work, we introduce linguistically motivated evaluation metrics designed to target these specific spoken-language phenomena. We apply them to analyse outputs from language models fine-tuned on spoken English and French, comparing their behaviour statistically with human dialogue corpora. Our findings highlight the value of these metrics for assessing the degree to which model-generated utterances resemble authentic human conversation.