We extend our previous algebraic formalisation of the notion of component-based framework in order to formally define two forms---strong and weak---of the notion of full expressiveness and study their properties. Our earlier result shows that the BIP (Behaviour-Interaction-Priority) framework does not possess the strong full expressiveness with respect to the sub-class of GSOS rules used for the definition of its semantics. In this paper, we refine this comparison detailing the expressiveness of classical BIP, Offer BIP and a number of variations obtained either by relaxing the constraints in the definition of priority models or by introducing positive premises into the rule formats used to define the operational semantics of composition operators. The obtained results are organised into an expressiveness hierarchy.