N2O is more stable than CO2.

Mixing N2O with water or cream won't create different molecules. If the liquid you add N2O is not very thick (like water) the gas and liquid will separate in two. If it is thick, as with cream, the gas will get trapped in it.

CO2 reacts with water (H2O) making H2CO3 (carbonic acid). It makes soda water, which has a slight acid taste, and get bubbles of released CO2 if the pressure of the soda water falls. CO2 can be used for whipping cream, but it will give acid taste to it, so NO2 is more suitable for most applications.

CO2 Produces the fizzy sensation found in carbonated drinks where as N2O will aerate cream as whipped.

None of them cools liquids. The chargers get cooled down when opened, as the gas inside them decreases pressure. But that gas goes to the cream whipper or the soda siphon, which theoretically should increase its temperature, but having a much larger volume than the charger makes that increase unnoticeable