Aspect-based sentiment analysis (ABSA) is a fine-grained sentiment analysis task that aims to identify sentiment toward specific aspects of an entity. While large language models (LLMs) have shown strong performance in various natural language processing (NLP) tasks, their capabilities for Czech ABSA remain largely unexplored. In this work, we conduct a comprehensive evaluation of 19 LLMs of varying sizes and architectures on Czech ABSA, comparing their performance in zero-shot, few-shot, and fine-tuning scenarios. Our results show that small domain-specific models fine-tuned for ABSA outperform general-purpose LLMs in zero-shot and few-shot settings, while fine-tuned LLMs achieve state-of-the-art results. We analyze how factors such as multilingualism, model size, and recency influence performance and present an error analysis highlighting key challenges, particularly in aspect term prediction. Our findings provide insights into the suitability of LLMs for Czech ABSA and offer guidance for future research in this area.