Electolysis of H2O to produce O2(g), in a small, portable unit
In scuba diving the main issue is pressure. To be able to breathe, you need to counteract the pressure of the column of water on your rib cage. This is why divers breathe from compressed gas tanks. Otherwise their rib cage and lungs would be crushed by the pressure. At higher pressures, air becomes too viscous to be breathed without too much effort, and the build-up of dissolved nitrogen in the tissues leads to narcosis ("being drunk"), so the oxygen has to be mixed with helium, that is much less viscous. So, with theses 'artificial gills' or with electrolysis, you still need a tank of helium, and a powerful compressor.

Overall, it is much more convenient to carry tanks of compressed mixtures of gases. Compressing gases is a form of energy storage (that could even power cars). But if you are in a nuclear-powered submarine, then you would be better off doing electrolysis.