Since the pioneering work of Embrechts and co-authors in 1999, copula models enjoy steadily increasing popularity in finance. Whereas copulas are well-studied in the bivariate case, the higher-dimensional case still offers several open issues and it is by far not clear how to construct copulas which sufficiently capture the characteristics of financial returns. For this reason, elliptical copulas (i.e. the Gaussian and Student-t copula) still dominate both empirical and practical applications. On the other hand, several attractive construction schemes appeared in the recent literature promising flexible but still manageable dependence models. The aim of this work is to empirically investigate whether these models are really capable to outperform its benchmark, i.e. the Student-t copula(which is termed by Paul Embrechts as ”desert island copula” on account of its excellent fit to financial returns) and, in addition, to compare the fit of these different copula classes among themselves.