Motivation: Students learning to program often reach states where they are stuck and can make no forward progress. An automatically generated next-step hint can help them make forward progress and support their learning. It is important to know what makes a good hint or a bad hint, and how to generate good hints automatically in novice programming tools, for example using Large Language Models (LLMs). Method and participants: We recruited 44 Java educators from around the world to participate in an online study. We used a set of real student code states as hint-generation scenarios. Participants used a technique known as comparative judgement to rank a set of candidate next-step Java hints, which were generated by Large Language Models (LLMs) and by five human experienced educators. Participants ranked the hints without being told how they were generated. Findings: We found that LLMs had considerable variation in generating high quality next-step hints for programming novices, with GPT-4 outperforming other models tested. When used with a well-designed prompt, GPT-4 outperformed human experts in generating pedagogically valuable hints. A multi-stage prompt was the most effective LLM prompt. We found that the two most important factors of a good hint were length (80--160 words being best), and reading level (US grade 9 or below being best). Offering alternative approaches to solving the problem was considered bad, and we found no effect of sentiment. Conclusions: Automatic generation of these hints is immediately viable, given that LLMs outperformed humans -- even when the students' task is unknown. The fact that only the best prompts achieve this outcome suggests that students on their own are unlikely to be able to produce the same benefit. The prompting task, therefore, should be embedded in an expert-designed tool.