If it's for a smaller child that will play with it roughly I would go with paint. I'd only go with embroidery if I thought the kid would take good care of the toy, since it's a lot of work to put down to have it be ripped apart.
But you should do what seems more fun and exciting for you. I think paint will be better for a bit more "realistic" feel, and embroidery for a more whimsical feel with some fun pattern.

But you should do what seems more fun and exciting for you. I think paint will be better for a bit more "realistic" feel, and embroidery for a more whimsical feel with some fun pattern.