Originally posted by KazetNagorra
Water contains less oxygen than air does. So the advantage is that obtaining oxygen is easier as long as the organism is always close to the surface.
My current reasoning on this, whether right or wrong, goes like this:
The rate at which a unit of O2 defuses through a unit surface area of lung/gill lining into the blood stream from external water/air is determined in part by whether the external media is water or air. Air may always have a higher concentration of O2 but, providing some water is fully saturated with O2, even though that water would have a lower proportion of O2, the rate at which a unit of O2 defuses from water through a unit area of gill lining into the blood stream should be about the same as the rate at which a unit of O2 defuses from air through a unit area of lung lining into the blood stream. This is just because of the way the physics of diffusion of gasses works.
So, this is why I assume that, providing the water is fully saturated with O2, there shouldn't be much advantageous difference whether the organism breaths air or water if the organism always stays close to the surface of the water.
Of course, water can be very far from fully saturated with O2, hence my hypothesis.