A turbocharger is better than an nitrous install because it works better and you don't have to refill it. But that's not all; a turbo also puts less load on the engine for the amount of power you get out.
Nitrous is stored as a liquid in the bottle but injected into the intake as a gas. Water/meth injection decreases EGTs because the water enters the combustion chamber as a liquid (droplets in suspension, we hope) and it is converted to a gas in the combustion chamber. This change of state requires a significant amount of heat energy which comes mostly from the combustion gases, thus keeping the cylinder cool and helping to reduce EGTs. Methanol is used not just to add fueling, but also it's there as antifreeze. You don't need it in hot conditions. Nitrous oxide is introduced as a gas and reacts with additional fuel which is where the additional heat comes from. Since it's not introduced as a liquid, it doesn't matter that it's a lot colder than the water; it has less mass and it also doesn't have to go from liquid to gas in the combustion chamber. As for N2O adding more O2 than a turbocharger can, with 11 pounds (which is about the peak you should try to get out of the IDI engine1) you get 11/14.7=~75% peak improvement in intake air.
Again, a turbo increases compression AND increases oxygen AND increases airflow, while nitrous only increases oxygen. A turbocharger DOES increase IAT due to compression, but the compression also has the effect of reducing EGTs at a given power output because you can reach the same combustion temperature with less fuel due to the increased heat of adiabatic compression, which is what makes Diesel engines work. Nitrous won't increase your compression, which is why it's at a disadvantage compared to turbochargers when it comes to EGTs.
Finally, splitting water into steam in the combustion chamber actually provides power itself, without producing any heat; indeed, the process of disassociating water into hydrogen and oxygen consumes heat. The heat energy is going to be given back from the water mostly in the exhaust system and then dissipated from there by conduction and near infrared radiation. Manufacturers claim up to 100 HP gains on water injection alone. Any significant increase in power output can only occur during periods of heavy load, as water injection can rapidly reduce combustion temperatures below working levels.
With all that said, it is often said that nitrous and turbochargers go together like they were meant to; the nitrous charge cools the turbine on the way in, and the turbo provides the high airflow. However, the only purpose of running a nitrous shot on top of turbocharging is to burn even more fuel, and the total system has to be able to accept the increased load.
- 1. This blurb was originally written for a Ford Diesel forum