DIY water chiller hydroponic co2 sealed grow room

In case of using Air Conditioning to cool the air directly inside the room the compressor pumps freon (or other refrigerant) through the coils of evaporator (the cold radiator of ac unit, which does the same thing as the ice box) and the air is blown over the evaporator of ac and is cooled. Meaning the evaporator component of ac unit is functionally identical to Ice Box.

Now water cooled option:
Water chiller is effectively exactly the same thing as an air conditioner, except that its evaporator coils (through which exactly the same refrigerant is pumped by the same compressor) cools water it is submerged into, instead of directly cooling the air like in the air conditioner. And then there is another circuit, which moves this chilled water through another evaporator coil (aka in hydroponic water cooling context as "Ice Box"), which in turn cools the air, thus doing what evaporator coil of the same water cooler could have done just as well (or more effectively) if it had this air blown though it directly.

Water chiller setup involves a redundant circuit of water circulating through another evaporator coil. This adds another coil, lots of extra tubing and an extra water pump.
Overall, I would imagine, that the thermodynamic efficiency of water chiller and ice box is probably very close to that of an AC unit. But it is redundant and involves many unnecessary components (therefore: more things to break down).