I guess their similarities compared to those of the animals are both of them are living organisms, both the animals and plants have the same needs:
they both need water in order them them to not dehydrate, carbon dioxide in order to breathe, and sunlight in order for their bodies to maximize their energy. To compare their systems; the mouth part of animals are same of the plant's root both
the root and mouth part obtain water in order to hydrate, the animal's nose and the plant's leaf get carbon dioxide to breathe, and so on and so forth.
This is only what i really know but hope these helps!!! ^_^