Hello MattPete,
Thanks for reaching out to Apple Support Communities. We see you have some questions about low quality when sending messages through Wi-Fi, but not cellular data. Have you tried getting closer to the router, or resetting the router, to see if this happens after? As this is only happening with your Wi-Fi, we'd recommend troubleshooting a few steps with your network, or try with another network, to see if the issue remains.
Also, be sure your iPhone is updated, with help here: Update your iPhone, iPad, or iPod touch - Apple Support
Regards.