Since their advent, supertrees have been increasingly used in large-scale evolutionary studies requiring a phylogenetic framework and substantial efforts have been devoted to developing a wide variety of supertree methods (SMs). Recent advances in supertree theory have allowed the implementation of maximum likelihood (ML) and Bayesian SMs, based on using an exponential distribution to model incongruence between input trees and the supertree. Such approaches are expected to have advantages over commonly used non-parametric SMs, e.g. matrix representation with parsimony (MRP). We investigated new implementations of ML and Bayesian SMs and compared these with some currently available alternative approaches. Comparisons include hypothetical examples previously used to investigate biases of SMs with respect to input tree shape and size, and empirical studies based either on trees harvested from the literature or on trees inferred from phylogenomic scale data. Our results provide no evidence of size or shape biases and demonstrate that the Bayesian method is a viable alternative to MRP and other non-parametric methods. Computation of input tree likelihoods allows the adoption of standard tests of tree topologies (e.g. the approximately unbiased test). The Bayesian approach is particularly useful in providing support values for supertree clades in the form of posterior probabilities.