There is an urgent need for a transition to healthy diets that can be produced in a sustainable food system. Different modelling approaches are used to understand what constitutes such sustainable healthy diets. Diet optimization and environmental food system optimization are modelling approaches that are developed from different angles, i.e. either starting from dietary changes or from food system changes. The aim of this study was to investigate the consequences of using a diet optimization model or an environmental food system optimization model on the healthiness, the environmental impact, the cultural acceptability, and the composition of modelled diets. To illustrate these consequences we used CiFoS (Circular Food System) and SHARP (Sustainable, Healthy, Affordable, Reliable, and Preferable diets) as case models. CiFoS is a biophysical environmental food system optimization model that allows to redesign the food system to produce a (healthy) diet for the current or future population within planetary boundaries. SHARP is a diet optimization model that is based on benchmarking and aims to calculate healthier and more sustainable diets that are acceptable for consumers. We found that both optimization approaches have unique applications in time scale (long vs short term solutions), geographic scale (national vs continental scale) and an individual versus a population approach. However, due to different approaches in calculating environmental impacts, accounting for co-products and biophysical boundaries in the food system, translating commodities into realistic diets, and considering cultural acceptability, modelled diets from these two approaches are not comparable. These findings show that, when used in the right context, both models provide unique insights in how sustainable healthy diets may be achieved, but also stress the need to understand the methodology behind models. This paper is an important step in strengthening the integration of different disciplines to make well informed decisions for healthy diets within planetary boundaries.