We compare the expressive power of a class of well-structured transition systems that includes relational automata, Petri nets, lossy channel systems, and constrained multiset rewriting systems. For each one of these models we study the class of languages generated by labelled transition systems describing their semantics. We consider here two types of accepting conditions: coverability and reachability of a given configuration. In both cases we obtain a strict hierarchy in which constrained multiset rewriting systems is the the most expressive model.