Oxygen dissolve in water
Carbon dioxide is not stable in water in its original form, so it undergoes an acid-base reaction to give the carbon dioxide.

On the other hand, oxygen is stable and soluble in water in its $\ce{O_2}$ form, so it will stay like that, no reaction other than solubilization. Besides, it could react with organic matter or other compounds in water, oxidizing them, and getting reduced to $\ce{OH^-}$