We present a set of three-dimensional direct numerical simulations of incompressible decaying magnetohydrodynamic turbulence in which we investigate the influence of an external uniform magnetic field B0. A parametric study in terms of B0 intensity is made where, in particular, we distinguish the shear-from the pseudo-Alfvén waves dynamics. The initial kinetic and magnetic energies are equal with a negligible cross correlation. Both the temporal and spectral effects of B0 are discussed. A subcritical balance is found between the Alfvén and nonlinear times with both a global and a spectral definition. The nonlinear dynamics of strongly magnetized flows is characterized by a different k⊥ spectrum (where B0 defines the parallel direction) if it is plotted at a fixed k∥ (two-dimensional spectrum) or if it is integrated (averaged) over all k∥ (one-dimensional spectrum). In the former case a much wider inertial range is found with a steep power law, closer to the wave turbulence prediction than the Kolmogorov one such as in the latter case. It is believed that the averaging effect may be a source of difficulty to detect the transition towards wave turbulence in natural plasmas. Another important result of this paper is the formation of filaments reported within current and vorticity sheets in strongly magnetized flows, which modifies our classical picture of dissipative sheets in conductive flows.