A study on the spatio-temporal dynamics of broad-area Nd:YAG (yttrium aluminium garnet), Nd-doped phosphate glass and Nd-doped silicate glass lasers is presented to show the influence of the inhomogeneous gain profile and cross-relaxation phenomena on the spatio-temporal dynamics of the system. The suppression of the order-disorder transition shown in Cabrera et al (2006 Opt. Lett. 31 1067) for homogeneously broadened class B lasers is found for both glass lasers, independently of the strength of the cross-relaxation mechanisms. The results obtained indicate that a higher degree of inhomogeneous broadening leads to suppression of the filamentation in the transverse intensity pattern.