In the last two decades, agricultural production intensity has become a subject of growing attention in the field of agricultural sustainability. Based on an empirical application for Swiss mountain dairy farming, the goal of our research was to better understand the relationship between agricultural production intensity, defined as the biophysical agricultural production per unit of land use area, and farm environmental performance. We thereby revisited the definition of production intensity and, more precisely, of the spatial system boundaries of its denominator. For that purpose, we analyzed the relationship between the “classical” production intensity indicator accounting only for the on-farm land use area and a cradle-to-farm gate intensity indicator encompassing off- and on-farm land use area. In a subsequent step, we investigated the relationship between farm environmental performance and the two production intensity indicator types. The analysis relied on the cradle-to-farm gate Life Cycle Assessments of 56 farm observations. Spearman’s correlation analysis revealed a very strong positive correlation between on-farm and cradle-to-farm gate production intensity. The definition of production intensity did not play a crucial role in the observed relationship between production intensity and farm environmental performance. Production intensity was positively correlated with farm global environmental performance. Conversely, it was negatively correlated with on-farm local environmental performance. By revealing this environmental trade-off associated with agricultural intensification, our findings highlight the challenging nature of achieving sustainable intensification simultaneously on the global and local ecosystem scales.