Ya Audacity would be perfect for that.
I have a rather old copy, its about two years old and it has a frequency analysis tool. It can only analyze about 30 seconds of a sound file but it does produce a pretty nice looking graph.
Even better, the frequency analyser has an export button that can output a text file with frequency and amplitude for the sound sample. You could create a graph using Excel from that text file that would show show the frequency trends of each pickup in an overlapping fashion for comparrisons. That would probably work the best IMO
All things being equal for pickup placement, and force of a strum I think it would work very nicely to make a point.