The integration of Large Language Models (LLMs) in Requirements Engineering (RE) education is reshaping pedagogical approaches, seeking to enhance student engagement and motivation while providing practical tools to support their professional future. This study empirically evaluates the impact of integrating LLMs in RE coursework. We examined how the guided use of LLMs influenced students' learning experiences, and what benefits and challenges they perceived in using LLMs in RE practices. The study collected survey data from 179 students across two RE courses in two universities. LLMs were integrated into coursework through different instructional formats, i.e., individual assignments versus a team-based Agile project. Our findings indicate that LLMs improved students' comprehension of RE concepts, particularly in tasks like requirements elicitation and documentation. However, students raised concerns about LLMs in education, including academic integrity, overreliance on AI, and challenges in integrating AI-generated content into assignments. Students who worked on individual assignments perceived that they benefited more than those who worked on team-based assignments, highlighting the importance of contextual AI integration. This study offers recommendations for the effective integration of LLMs in RE education. It proposes future research directions for balancing AI-assisted learning with critical thinking and collaborative practices in RE courses.