Background/Objectives: Artificial Intelligence (AI) technology is gaining attention for its potential in cognitive function assessment and intervention. AI robots and agents can offer continuous dialogue with the elderly, helping to prevent social isolation and support cognitive health. Speech-based evaluation methods are promising as they reduce the burden on elderly participants. AI agents could replace human questioners, offering efficient and consistent assessments. However, existing research lacks sufficient comparisons of elderly speech content when interacting with AI versus human partners, and detailed analyses of factors like cognitive function levels and dialogue partner effects on speech elements such as proper nouns and fillers. Methods: This study investigates how elderly individuals’ cognitive functions influence their communication patterns with both human and AI conversational partners. A total of 34 older people (12 men and 22 women) living in the community were selected from a silver human resource centre and day service centre in Tokyo. Cognitive function was assessed using the Mini-Mental State Examination (MMSE), and participants engaged in semi-structured daily conversations with both human and AI partners. Results: The study examined the frequency of fillers, proper nouns, and “listen back” in conversations with AI and humans. Results showed that participants used more fillers in human conversations, especially those with lower cognitive function. In contrast, proper nouns were used more in AI conversations, particularly by those with higher cognitive function. Participants also asked for explanations more often in AI conversations, especially those with lower cognitive function. These findings highlight differences in conversation patterns based on cognitive function and the conversation partner being either AI or human. Conclusions: These results suggest that there are differences in conversation patterns depending on the cognitive function of the participants and whether the conversation partner is a human or an AI. This study aims to provide new insights into the effective use of AI agents in dialogue with the elderly, contributing to the improvement of elderly welfare.