Over the last decades, livestock farms' sizes have increased in Western Europe although the benefits obtained by the farms and agricultural workers are far from being obvious nor demonstrated. The purpose of this paper is to propose the use of functional regression to study the relationship between farm size and farm performance trends in long-term panel data. While a linear Partial Least Squares regression is performed as a reference model, a regression for functional data enrich the modelling with the chronological information contained in panel data, in particular evolution shapes of performance and size. The proposed methods are applied on a long-term structural, technical and economic database of cattle beef farms in the Charolais region (France). The achieved regression models, whether classical or functional, suggest that, in our case study, the farm size is not sufficient to explain its performance. We now expect our work to be a starting point for further analysis. In particular, other structural, economical and technical characteristics could contribute to better model livestock farms' evolution.