The short answer
The Mamaroo is the premium choice: five motions that combine up-and-down with side-to-side, four sounds, and control from the UPPAbaby app, Alexa or Google Home. The Cassia is smaller and lighter, swings front to back or side to side, rotates 360 degrees and starts swaying on its own when it senses fussing.
The Mamaroo wins on the quality of its movement and its three-year warranty. The Cassia wins on practicality: it weighs 4.5kg, runs on mains or AA batteries and costs around £180, or less on offer, against about £320.
My call: the Cassia for most families. Pick the Mamaroo if you have the space, a socket to spare and a baby who clearly prefers being bounced to being swung.