Plush wins on price per unit at volume, on hand feel and on perceived safety for younger age grades. It loses on silhouette: fabric rounds off sharp design lines, embroidery has a minimum stroke width, and complex appendages get simplified whether the designer agrees or not.
Vinyl wins on shelf presence and on silhouette fidelity. A vinyl figure holds the shape the illustrator drew, which is why collectible and display-driven programmes almost always go that way. It loses on cost at low volume, because tooling has to be paid for before the first unit exists.
The channel decides. Gift-with-purchase and promotional programmes usually want plush: low unit cost, light shipping, no tooling amortisation. Retail collectibles and licensing programmes usually want vinyl: the object has to look right on a shelf next to a much more expensive competitor.
If the budget allows only one, ask which failure is cheaper. A plush version of a detailed character looks soft and loses detail; a vinyl version of a cuddly character looks cold and unholdable. Neither is wrong — but only one of them will match the promise the packaging makes.