This study discusses the differences and similarities in the mechanisms of reduction of instability in free shear flows induced by polymer and fibre additives. We present results of a linear stability analysis of the mixing layer at high Reynolds numbers, and include the effects of the presence of polymers or rigid particles on the temporal instability of the flow. The examination of profile contours of different perturbation terms and the analysis of the rate of production of enstrophy revealed two fundamentally different mechanisms behind the reduction of the instability in each case. For a fibre suspension with hydrodynamic interactions, the shear stress disturbance induced by the misalignment of the fibres, is the main driving term behind the decrease of the flow instability. On the other hand, the normal stress disturbance acts as a destabilizing factor. In the case of highly viscoelastic polymers, we show that the already known stabilizing role of the normal stress disturbance is counterbalanced by the destabilizing role of the shear stress disturbance. The reduction of the flow instability is in this case attributed to a change in the mechanism of convection of the base state vorticity by the velocity disturbance.