Polygenic indices (PGIs) are increasingly used to identify individuals at high risk of developing diseases and disorders and are advocated as a screening tool for personalised intervention in medicine and education. The performance of PGIs is typically assessed in terms of the amount of phenotypic variance they explain in independent prediction samples. However, the correct ranking of individuals in the PGI distribution is a more important performance metric when identifying individuals at high genetic risk. We empirically assess the rank concordance between PGIs that are created with different construction methods and discovery samples, focusing on cardiovascular disease (CVD) and educational attainment (EA). We find that the rank correlations between the constructed PGIs vary strongly (Spearman correlations between 0.17 and 0.94 for CVD, and between 0.40 and 0.85 for EA), indicating highly unstable rankings across different PGIs for the same trait. Simulations show that measurement error in PGIs is responsible for a substantial part of PGI rank discordance. Potential consequences for personalised medicine in CVD and research on gene-environment (G×E) interplay are illustrated using data from the UK Biobank.