We investigate how text genre influences the performance of models for controlled text simplification. Regarding datasets from Wikipedia and PubMed as two different genres, we compare the performance of genre-specific models trained by transfer learning and prompt-only GPT-like large language models. Our experiments showed that: (1) the performance loss of genre-specific models on general tasks can be limited to 2%, (2) transfer learning can improve performance on genre-specific datasets up to 10% in SARI score from the base model without transfer learning, (3) simplifications generated by the smaller but more customized models show similar performance in simplicity and a better meaning preservation capability to the larger generic models in both automatic and human evaluations