In terms of quality, the difference between quality of ray tracing engines is mostly up to the user at this point. People who have zero experience with Manta Ray won't be able to do better renders than people with non-zero experience with Cycles, and vice-versa. Same goes if you use Renderman, V-ray, POV-Ray, Mental or any other renderer. In capable hands, they can all do absolutely wonderful renders, but again, mostly up to the user rather than the engine.

In terms of user experience, if you're using Blender, it's much easier to use Cycles as it's already integrated in Blender, while Manta Ray is a standalone renderer.

Blender is not itself a renderer. It comes with (at least) two built-in renderers, Eevee and Cycles, and can be interfaced to many others.