Where Halliday (1985) justifies his process types largely on the basis of configurations of Agent, Process and Medium, Hasan additionally draws the Beneficiary role into the picture.
The system of process types isn't justified on configurations of Agent, Process and Medium. Each of these — process types, on one hand, configurations of Agent, Process and Medium, on the other — represents a distinct complementary perspective on transitivity: the transitive and ergative models, respectively.
The transitive model is concerned with the ways in which processes are different, with each type of process 'characterised by process-participant configurations where the functions are particular to that type' (Halliday & Matthiessen 2004: 280).
The ergative model, on the other hand, is concerned with how the process types are all alike; how 'they all have the same grammar' (Halliday & Matthiessen 2004: 281).