We present generic outcomes of collisions between stable solitons with intrinsic vorticity S=1 or S=2 in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, for the axially symmetric configuration. An essential ingredient of the complex Ginzburg-Landau equation is an effective transverse diffusivity (which is known in models of laser cavities), as vortex solitons cannot be stable without it. For the sake of comparison, results are also included for fundamental three-dimensional solitons, with S=0. Depending on the collision momentum, χ, three generic outcomes are identified: merger of the solitons into a single one, at small χ; quasielastic interaction, at large χ; and creation of an extra soliton, in an intermediate region. In addition to the final outcomes, we also highlight noteworthy features of the transient dynamics.