Direct numerical simulations of three-dimensional compressible Navier-Stokes equations are conducted using high-order numerical methods in cylindrical coordinates. Aim of the work is to examine the effect of three-dimensionality in the dynamics of vortex breakdown in swirling jets within a specific range of Reynolds numbers. The main elements of vortex breakdown are revealed in our computations, and the interaction between three-dimensional helical instabilities and the axisymmetric process of breakdown is discussed. The results confirm a general tendency of swirling flows to burst into a sequence of bubbles when the Reynolds number is increased. Comparing axisymmetric and fully three-dimensional computations, it's observed the possibility that a single or double helical structure arising in linear regime can work to extract energy from the axisymmetric waves.