Let me start by saying I won't use a disc piezo. I will only use an under saddle rod piezo which is what is used in an electrified acoustic guitar. Some CBG's have the piezo wired direct to the out put jack, and the volume and tone are controlled on the amp. I strongly recommend using a pre-amp (on board or external) with a piezo. I most often use a built in pre-amp such as an electric acoustic has. With this setup the volume and tone can be controlled on the guitar.
A piezo pickup is designed to reproduce the natural acoustic tone of the instrument, and some people believe it achieves a more "authentic" CBG sound. You can use acoustic or electric guitar strings but acoustic strings will sound best when playing unplugged. Because it is built into the bridge under the saddle and therefore invisible, it won't interfere with any graphics on the box or dampen the acoustic properties of the top.
NOT SO GOOD
A piezo is more prone to howl or feedback, especially at high volume. If the CBG is not equipped with a preamp to smooth out the sound a piezo can sound somewhat harsh and brittle with poor bottom end response. The preamp is powered by a 9V battery which can be a pain if the battery dies without having a backup available.