It's a simple thing to prove. Just datalog the two. I always see around ambient with my turbonetics A2A. On the blow off valve subaru sound we're not really trying to sound like a suburu either, just make the most effective horsepower possible.
That would require sizing the systems the same. Let's say for example the A2A IC is the same size as the A2W HE. Then you have to decide what flow rate the water will be moving at. Most kits are about 5gpm, and that's way too slow. On the flip side I have run them up to 27gpm, which is significantly more ability to transport heat. And lastly unless both systems are tested with the same type of sensor in the same location (intake runner) the data can't be compared. And as far as I know none of the A2A systems have the same type of sensor as the A2W systems and they aren't in the intake runner. So really, it would have to be one hell of a test to get anything but junk data.
Something I did just look up. Water is 784x denser than air. That gives water a HUGE advantage when it comes to transferring heat. It transfers heat about 20x faster.
In a practical sense what I am seeing is that the out of the box A2A systems do a better job of keeping IAT's in check up to a certain boost level. Let's say that's 12psi. Then guys start getting bigger IC's. But eventually you run out of room and can't go bigger. I only have one piece of data on this but White Pony was having IAT issues with a big aftermarket A2A at I think it was 17-18psi (he was sampling at the intake runner). That seemed about the limit of ability to transfer heat with what you can fit in the front of the car.
Out of the box A2W systems are garbage because they're not sized correctly. But when sized correctly (lots of water flow, big heat exchangers, etc) they work incredibly well. Well past 17-18psi where the A2A can't control temps.
This is another case, as are many, where there is no "best". It will depend on circumstances, use, etc. That said the OP that got this discussion going by stating:
Paxton uses an air to air intercooler not a heat exchanger. They are more efficient than water cooled intercooler and don't heat soak so easily.
I simply said that was false. Which it is. Water transfers heat about 20x faster than air because of its density. I was addressing the sweeping
"efficiency" statement only.
A statement like “In most cases at realistic boost pressures A2A systems work in Mustangs better than A2W systems do” is a statement I agree with 100%. But that is because most A2W systems are sized really bad, not because the science isn’t there.
As usual I'm being pedantic. The suggestion by the OP is correct in most cases.