The work aims to explore the advantages and limitations of human-agent collaborative conceptual design and measure how LLM-based agent influences designers' cognitive processes, design outputs (performance) and collaboration experience by integrating neuroscience, physiology, and social science paradigms. A conceptual design agent was developed with GPTs. 30 participants were randomly assigned to human-agent and human-human groups for a 10-minute conceptual design task comparison. In terms of cognitive processing, the collaboration with the agent significantly enhanced participants' brain cognitive resource synchronization while reducing cognitive load and physiological skin conductance levels. The human-agent collaboration demonstrated higher ideation fluency, whereas human-human collaboration exhibited stronger originality in design outputs. Participants generally acknowledged the agent's exceptional information retrieval and processing capabilities, reporting lower stress levels during collaboration. However, the agent required participant-led decision-making and showed limitations in communication efficiency and trust compared to human collaborators. In conclusion, LLM-based agent currently demonstrates clear advantages in enhancing the cognitive efficiency and creative output of designers, as well as in stabilizing their workload and emotional well-being. However, there is still room for improvement in terms of originality, communication efficiency and trust.