Should there be a difference in sound quality between Chromecast and AirPlay?

Yes, there can be depending upon streaming service being used, and also due to the fact the source for AirPlay is your mobile device, while with Chromecast the mobile device is only the controller connecting the Prisma module directly to the streaming service over the network. This is also the reason that AirPlay is a little slower to respond to commands. Finally, Chromecast is capable of higher resolution up to 24/96 kHz, depending upon what the streaming service is providing, of course. AirPlay 2 is limited to 16/44.1 and actually downgrades the lossless stream from Apple Music to AAC 256kbps, even though AirPlay 2 is actually capable of lossless playback with other streaming service applications, such as Qobuz.