Response design plays a critical role in user experience in spoken conversational search (SCS). This study examines how two response styles—long response presentation (LRP) and short response presentation (SRP)—affect users’ cognitive load and search behavior under different task complexities. A user study ( \(N=139\) ) was conducted using an LLM-based voice agent across low and high complexity search tasks. Results show that SRP reduced cognitive load and improved satisfaction, especially for low complexity tasks. However, in high complexity tasks, SRP led to more query issuance. This may indicate that users were actively engaging with the fragmented information to better understand the task or fill in missing details. These findings suggest that no single response style is optimal across all situations.