Large language models (LLMs) have been found to be a support for modeling tasks in various application areas, including enterprise modeling (EM). In EM, LLMs can be applied to help domain experts create models efficiently that adhere to the correct syntax of the modeling language. In this context, how to organize the interplay of the domain expert and LLM is an important topic. Should the domain expert get an LLM-generated model and improve it (LLM-first) or should LLMs be used to improve models developed by domain experts (domain expert-first)? The paper investigates the interplay between domain expert and LLM by investigating three different application examples and conducting quasi-experiments. The results also contribute to determining the potential and limits of LLMs in EM.