The relay board is safer and has protection against spikes common with relay controlled outputs. However, you could add a flyback diode for protection if you just want to do that. Keep in mind though the Sounder output is rated up to 1 amp total so if nothing else is drawing power you "could" directly drive the siren.
Let me add something technical here, related to the OP output relay and trying to "save" an output.
You can use a demux circuit to expand your outputs to 128 outputs on the OPII (up to 256 outputs if you're creative) so likely one would never have to worry about using up all the outputs on any Omnipro of any model. Using just three (3) outputs will allow a demux circuit to drive up to 8 outputs which could be a solid state relay bank, multi-zone sprinkler controller, high voltage lighting, pool pumps, etc.. . Some of a 2¢ comment