Two kinds of behaviour are commonly distinguished among porous architectured materials: stretching-dominated and bending-dominated ones. One or the other is favoured depending on the mechanical application. This property has been widely studied for random foams and periodic lattices, but has not yet been considered for quasi-periodic ones. Generally speaking, few studies have investigated their mechanical behaviour, and when this has been done, the impact of the elementary pattern shape has not been considered. In this paper we propose a classification of quasi-periodic structures depending on their dominance type by performing numerical simulations on mesoscopic models, and analysing the proportions of the strain energy stored in stretching and bending. As a result, three different dominance behaviours can be distinguished: completely stretching or bending dominated and varying dominance. Belonging to one or the other category depends mainly on the elementary pattern shape, and thus so does the overall mechanical behaviour.