A lot of work exists on notions of equivalence and soundness relations of different workflow models, which are used in different domains like e.g. Business Process Modeling, Software and Service Engineering. These definitions are based on different models, including Petri Nets and different versions of Finite State Automata, having different expressiveness and computational complexity classes. The aim of this paper is to compare the equivalence and soundness relations of the Petri Net and annotated Finite State Automaton models in the context of Service Oriented Architectures. It turns out that up to a certain expressiveness the relations are comparable and computable with reasonable effort. For these cases also mappings between the different models and relations are presented.