The aim of this study is to explore how large language models (LLMs) integrated with structured versus unstructured concept generation techniques (CGTs) influence designers’ creative thinking processes and outputs. Using human–human collaboration (HHC) as a baseline, a 2 × 2 mixed factorial design was adopted to investigate the effects of collaborator type (between-subjects: LLM-based agents vs. experienced designers) and CGT type (within-subjects: brainstorming vs. TRIZ). Two LLM-based agents, IntelliStorm and EvoluTRIZ, were developed for the study, with 32 participants randomly assigned to either the HHC or human–agent collaboration (HAC) groups. Brain activity was measured using functional near-infrared spectroscopy, while outputs were assessed through expert evaluations. Results showed that designers exhibited lower cognitive load, better cognitive resource coordination, and enhanced fluency and flexibility in thinking in HAC than in HHC. Moreover, distinct patterns were revealed in different CGTs: brainstorming activated the right dorsolateral prefrontal cortex (PFC) as the core connectivity region, enhancing ideational fluency, whereas TRIZ activated the left dorsolateral PFC, facilitating refined thinking. Although HAC demonstrated stronger overall performance, HHC retained unique advantages in originality. This research offers novel neuroscientific insights and provides evidence-based guidance for developing more effective LLM-based design agents.