Hoping this post will help a little. If your example isn’t an Audi you might as well throw your results out the window. As a tech for SVT Ive learned that there are many a new variable when trying to simplify the results from a large displacement low RPM motor to the small displacement high rpm motors.  The euro motors actually run about 50 to 60+ deg hotter then most domestics. That is a large impact to start from.
People use Air to water intercooling systems for there ability to drop charge temps below ambient. That is kinda the concept of them. That you can pull out more heat due to the large temperature variance.
Using ice in a recirculation storage system  can bring the temps down well below even 40deg. Dry ice can bring temps down to even -0
This needs to be used in conjunction with a proper exchange unit and size.
Also Chemical cooling helps but I would be careful at saying its better. There are many variables to both. Still remember the methanol absorbs the heat but its not dissipated till its removed from the system. A large part of that system is closed and will carry the heat with it. Law one of terminal dynamics.
The point.
Is, just like a intercooler needs to have enough surface area and temp charge to cool the charge. You also need to have an abundance of methanol to exceed the transfer of heat needed to be impacted by the addition of the fluid to the charge heat raito… Sorry for the hard read on the last part.
Bottom line. They both work. But what is more efficient. That is difficult to say. In this case you would need so much methanol to cool the intake temps that you would just be better off taking out the injectors and just spraying straight methanol across the air charge.  and using that much methanol you might as well just use it as fuel.