The advantages with a charge cooler are that water has a much higher heat capacity than air as a cooling medium so a cooler cooled by water can be much smaller to shift a given amount of heat from the charge. In addition, you can locate it on the engine rather than where you have cooling airflow. It'll be more free-flowing and tie up a smaller volume of air in the cooler than an intercooler, hence reducing turbo lag.

I ran an air-water system on the MR2 for those reasons; better packaging (it's hard to locate an air-air cooler effectively on a rear engine car) and better charge temperatures during extended boost periods (i.e. on track) thanks to the large volume of water in the system (as the water rad was at the front of the car, in front of the regular engine radiator).
Worked well, though a good chargecooler is rather expensive (I think I paid ~£500 for my PWR barrel - I was never that convinced that the cheap 'square' ones on eBay were all that good, flow wise)