Turbo lag shouldn't be a priority to determind going A:W for cooling IMO. Because I doubt you can even measure a difference in most cases, much less a substantial difference.
However, super cold charge air, is like having another turbo stage
The more you can cool the intake air post turbo, the more air the system takes in through the compressor inlet. Yes, actually more airflow.
You can actually cool the air sooo much that your turbo is now undersized for the flow reaquirements. Or conversely, if you take a turbo that is properly sized for an engine with good charge air cooling, and you remove the cooling, you will very often have a turbo too large for the engine now. Resulting in surging and compressor efficiency losses, as well as overboosting.
Intercooling moves more air through the engine. W:A can do that with amazing levels of efficiency for short term duration where a reservoir can be used for the cooling medium. But for durated runs, you simply revert back to the same basic efficiency as an A:A with the water simply serving as the medium between charge air and ambient air at the front mounted exchanger.
Dropping charge air temp is just as powerful as adding boost as far as CFM flowing into the charger. It's just much harder to actually get the charge air temps to come way down, whereas it's very easy to run the boost up.
I have often thought of making my own intake manifold with an integral W:A core inside. More plenum volume as well. But, things are a taaaad tight in there on a powerstroke, lol.