Who each product is really for
Ringy
Ringy is generally described as a CRM with calling and messaging built in, aimed at agents and small sales teams working large lead volumes, particularly in insurance and similar high-contact markets. The appeal is singularity: one login, one contact record, one place where the outcome of a call lands. For a team without an entrenched CRM, that removes a whole category of integration problems.
Kixie
Kixie is usually positioned as a sales dialing and telephony layer designed to work alongside an existing CRM rather than replace it. The appeal is leverage: keep the system your business already runs on, and add calling power, automation and call analytics on top. For teams with a CRM they are committed to, that is a much smaller change than a platform migration.
Both vendors adjust scope over time, so confirm current positioning directly before you shortlist.