One isn't susceptible to heat-soak.
They both are susceptible to heat soak eventually. With an A2W, the water heats up and the intercooler looses efficiency. For short durations (drag racing, etc.) an A2W can be a better solution.
A2A never runs out of ambient cooling air because it dumps heat into a continually renewed supply of air. A2A is easier to install, weighs less, isn't prone to leaks, and requires no maintenance.
A2A plus a cooling mist is probably the best of both worlds. I run a very small nozzle externally on the front of my A2A with 50% distilled water / 50% methanol with a nice decrease in IATs. (See data log here:
http://www.lotustalk.com/forums/f25/really-light-stuff-water-methanol-injection-55666/index2.html#post1104728 )
Another big advantage of the A2A for some is the ability to return a car to stock in about 30 minutes.
Depending on your goals, one solution will be better than the other.