The OEM airbox/intake snorkel is a "cold air" intake system that only inhales cold air from outside the engine compartment. The exit of the airbox has a nice bellmouth (aka "velocity stack") cast into it and its diameter is matched to the bellows behind it. For feeding air to the stock throttle body, that combination is going to be hard to beat. Exit opening in OEM airbox lid:
The entrance of the airbox is 10% larger than the exit so it sounds like a well balanced design. The stock intake snorkel that feeds the airbox doesn't seem ideal from a horsepower perspective, however. The OEM intake opening of the snorkel (where it sucks air in) is smaller than its exit so for the airbox, it's a bit like breathing through a straw. Also, the relatively tight curves of the snorkel are more difficult for the air to flow through than straighter designs. Despite that, the diameter of the OEM snorkel is still large enough that stock NSXs supposedly see no gains by replacing it with other snorkels and the OEM design will keep more dirt and water away from your air filter than any other "cold air" design I've seen.
To give you an idea where bottlenecks could be, here's an overview of the cross sections along various points of an NSX's intake tract:
Replacing the OEM intake snorkel with the Downforce air intake scoop will funnel all air entering the side intake into your airbox. With that, you'll have not only a "cold air" intake like stock but what could be called a "ram air" intake as well. You supposedly don’t really get a "ram air" effect at road car speeds but the entrance of the Downforce intake scoop is a lot larger than its exit and the flow into the airbox will be as smooth as possible. So whatever weaknesses the OEM intake snorkel has from a horsepower perspective should be cured with the Downforce scoop and it'll make the car's induction sound a lot louder. On the negative side, it will not only channel air into your airbox as efficiently as possible, but also dirt and water as well.
Comptech's offering not only modifies the intake snorkel but also the airbox itself by increasing the size of the airbox's entrance opening. Entrance opening in bottom half of Comptech airbox:
With a Comptech airbox, the engine doesn't only breathe through the round opening in the side wall you can see above but also through the opening around the gas tank pipe. How much it really helps if the airbox's entrance is that much larger than its exit, I don't know. There's an extension to the airbox that seals it against the side wall so like OEM, it's a true "cold air" design that only breathes cool air from outside the engine compartment. Inside the fender, there's a little hood but not a funnel like the Downforce air intake scoop so the Comptech offering shouldn't be called a "ram air" design.
Other offerings like the Downforce STACK intake system get rid of the airbox completely. Considering the smooth air path, gently increasing cross section, and bellmouths in a stock airbox/Downforce intake snorkel combination, the only way I can see how the STACK intake system is going to pose less of a restriction is if the filter itself lets air through more easily. Since the surface area of the STACK filter looks smaller than that of the stock filter, that's probably only going to happen if the filter element doesn't filter as well.
Other designs don't only inhale cold air from the fender but also warm air from the engine compartment. By definition, those are neither "cold air" nor "ram air" intakes. Inhaling air in the engine compartment probably doesn't make much of a difference on a dyno when the engine compartment lid is open. When you're actually driving on the road with the engine compartment lid closed it may be another story. Warm air is less dense, contains less oxygen, and produces less horsepower.
For the sake of my engine, I don't want it to inhale dirt and dust that will increase wear and decrease its lifespan. If I were planning on getting a supercharger, I'd want a cold air intake that minimizes the intake restriction as far as possible while still filtering the air well. If I didn't care how quickly the filter gets dirty, I'd keep the stock airbox and just slap on a Downforce air intake scoop. If that turned out to be too loud, I'd modify the OEM intake scoop and put that back on. If you unplug the resonator from the stock intake snorkel, you'll get a second intake opening. Put a bellmouth over that to smooth the airflow and your two intake openings together will be larger than the exit, reducing the restriction. It won't be as loud as the Downforce snorkel but it will be louder than stock, have less restriction than stock, be a true cold air intake, and still filter the air well.
If you're staying naturally aspirated, another area to consider beyond intake air temperature and restriction is the resonant frequency of the airbox/air filter system. Resonances can help push more air into the cylinders as the intake valves open. Perhaps the stock airbox doesn't have an ideal resonant frequency and if that's the case, perhaps it's because of packaging or servicing considerations - don't know. I do know that ProSpeed calculated what they thought would be a good resonant frequency and a designed an air filter/intake snorkel to deliver that. It's a long tube that snakes into the fender well and places a conical air filter behind the rear wheel. It looks like it should have a low restriction and breathe cold air plus have a different resonant frequency than stock. It also looks like it will be more difficult to service and might get dirty more quickly. If there's a supercharger in front of the intake valves, I don't think the resonant frequency of the air filtration system is going to help push more air into the cylinders. If done right, it could in a naturally aspirated engine - and maybe the OEM airbox leaves some horsepower on the table in that regard. Don't know.