In this paper, we present a comparative study of the emission properties of line sources embedded in two-dimensional finite-size aperiodically-ordered "photonic-quasicrystal" slabs made of dielectric cylinders arranged according to representative categories of aperiodic tilings. Our study, based on a rigorous full-wave numerical method, indicates the possibility of achieving directive low-sidelobe emission at several frequencies. In this connection, parametric studies are presented, and similarities and differences with the periodic case are highlighted.