Generative artificial intelligence (GenAI) is rapidly transforming the way students learn, create, and demonstrate knowledge in higher education. While universities are developing policies and guidelines, less is known about how students in specific disciplines perceive and use these tools. Here, we provide an explorative case comparison study and investigate engineering students' engagement with GenAI across two Australian universities. A survey of 131 students examined reported GenAI use, perceived benefits and challenges, and awareness of institutional policy and training across two cohorts with different demographic and curricular contexts. Our results showed broad awareness and adoption of GenAI, with differences between cohorts in reported frequency and purposes of use, as well as in perceptions of policy training. Students reported benefits in idea generation and efficiency while identifying challenges related to accuracy, content relevance, and ethical use. Our findings suggest that GenAI literacy development should be gradual, discipline-specific, integrated into coursework, and guided by clear communication about the ethical use of GenAI. The study highlights the importance of aligning institutional strategies with students lived experiences of GenAI in learning.