The globalisation of higher institutions has led to the emergence of EMI courses offered by faculty with diverse cultural and linguistic backgrounds. Existing literature has revealed that the cultural and linguistic backgrounds of English language teachers affect their teaching behaviour. However, this issue is relatively under-explored among EMI content teachers. This study explored 101 Chinese undergraduate students' perceptions of two categories of content teachers -- native English-speaking EMI teachers and local (non-native English-speaking) EMI teachers -- regarding their teaching behaviour and practices. Their perceptions were collected via a questionnaire survey and interviews, which were then triangulated by class observation of teachers' actual practices. Specifically, the students perceived that native English-speaking teachers adopted more interactive teaching approaches with diverse activities and various modalities of communication, but lacked intercultural competence. In comparison, local teachers obtained intra-cultural competence and thus could communicate with students about their learning difficulties. Their instruction was more intelligible but rather teacher-dominated. Students favoured interactive and efficient EMI courses with a primary focus on content. The findings provide insights for the implementation of the EMI curriculum and the development of EMI teachers' expertise.