This paper presents a comparative study of two approaches to automated assessment of Czech spoken language exams for non-native speakers: one using large language models applied to transcripts, and the other based on pre-trained speech encoder models. To our knowledge, this is the first study to explore automatic speaking assessment (ASA) for the Czech language. We evaluate both methods on a dataset of authentic high-stakes oral exams, annotated with binary pass/fail labels and total exam scores. Our best-performing models reach a QWK score of 0.65. Our experiments demonstrate the feasibility of applying ASA techniques in Czech and illustrate challenges related to data scarcity, transcription quality, and performance variability between input types.