the thing is co2 in a gas state is very cold thus giving a similar effect of dice or ln2. the advantage being if it is run in somewhat of a loop is that you will not have to refill all the time and the temp will stay constant
CO2 is not cold in a gas state. It's part of the make up of air. In fact you create it when you breath out. Dice is solid CO2. There's no magic with CO2, it heats up just like anything else.
Dice, LN2, LHe2, etc all use cold objects as sinks. LN2 is very cold, and absorbs large amounts of energy as it phase changes to a gas. However, the LN2 is not captured and converted back to a liquid by a compressor. If you want a true "extreme" long term system, that would be required. Although if I went through all the expense (thousands of dollars) to do that, I'd probably build a liquid helium system. But then again, water cooled SR-2 with dual 6 core Xeons starts looking cheap by comparision. And very few people have both problems and money to go beyond a WC SR-2 setup.
LN2 isn't actually cold, its the same effect as you're compressor: grab it when its gaseous, compress it to liquid, at which point its hot, cool it off, and now you've got a pressurized substance thats at room temperature. Then instant you release it from that pressurized environment, it jumps straight back to gaseous phase, which makes it stupidly cold. Ironically it also supersaturates the air at 1atm, meaning you can actually pool the liquid if it doesn't have a huge surface area, which is exactly what those LN2 coolers are doing. Its the process of evaporation that makes LN2 cold, not the LN2 itself. Its really very similar to alcohol, just, much more potent.
The LN2 in liquid form is cold even in the pot. If it was simply the act of boiling that lowered the temperature, then we'd just boil water and the water would get colder and well, yeah...
LN2 coming out of the container is chilled. The phase change simply provides the energy sink, not the cooling.