This document is a comparative study of four methods (Markov chains, compound processes, substructure factorization and generating functions) to compute the moments of probability distributions associated to homogeneous branching processes. Although all these methods have their own interests, the generating functions seem to be the most appropriate tools for this kind of probability model. In order to compare them, each method is first described and then applied to an example of multitype branching processes: the evolution of the number of active buds for a particular GreenLab plant growth model. Finally, the methods are listed according to their effectiveness.