I was soldering a lot of piezos today and decided to redo a test I did years ago. With a sharp pair of scissors I cut the disk into quarters.
As an unscientific test, I used duct tape to adhere them to the top of the Alley Cat. The results were the same as in my tests years ago - they both worked and the difference was very small, if any. (The Alley Cat sounded awesome!)
Volume and fidelity appeared to be the same. Bass response didn't fall. Box noises were the same. In my research and testing over many years it's my opinion that the difference in the size of the piezo lies mostly as an output device (buzzer, speaker, etc), not as an input device like we use them.
For any folks who work with piezos and didn't know, they can be cut down and still work. Some people do it to fit in a specific space, others do it to stretch their budget.