Recent work on Speech-to-Text Translation (S2TT) has focused on LLM-based models, introducing the increasingly adopted Chain-of-Thought (CoT) prompting, where the model is guided to first transcribe the speech and then translate it. CoT typically outperforms direct prompting primarily because it can exploit abundant Automatic Speech Recognition (ASR) and Text-to-Text Translation (T2TT) datasets to explicitly model its steps. In this paper, we systematically compare CoT and Direct prompting under increasing amounts of S2TT data. To this end, we pseudo-label an ASR corpus by translating its transcriptions into six European languages, and train LLM-based S2TT systems with both prompting strategies at different data scales. Our results show that Direct improves more consistently as the amount of data increases, suggesting that it may become a more effective approach as larger S2TT resources are created.