This question opens up a whole new can 'o worms, not that it doesn't need opening! [strike]Worms are people, too[/strike].
Buddhism (and it's forebear, proto-Hinduism) has had 'greater respect' for the non-human Earth life that precedes the Abrahamic religions. You could say that the differences they do take into account are not 'image' differences, but qualitative differences based upon
sentience. Sentience is the ability to feel, perceive and subjectively experience.
Western religious thought, on the other hand, has for almost as long held that "God" is separate from God's creations. Therefore, man, made in God's image, is similarly 'separate' from the world and it's denizens. So, in two geographically distinct areas, we have completely different orientations. Hmm, is one of them wrong and the other correct?
Forty years of wondering about this stuff (I was ten when I remember climbing library shelves for 'adult' books on mysticism and the like) and having close and enduring relationships with a variety of mammals, avian critters, and even bugs, I have convincing evidence of their sentience, along a continuum. Clearly the 'animal rights' folks (in all their possible iterations) are taking a similar tack.
Whether I'm an animal like a chimp or not, we share sentience, to a degree, with non-human beings. Higher mammals, higher quality/quantity of sentience, and as life forms simplify, their quality of sentience also simplifies. Feeling sorry for the worm eaten by a robin is silly, as the worm doesn't have the neurological structures giving rise to a sense of a self that doesn't want to be eaten. But feeling sorry for a cow in a slaughterhouse is a natural sympathy, it doesn't have to be taught.
Dividing planet Earth's life between humans and 'all the rest' is rapidly becoming less acceptable or necessary, as evidenced everywhere you look, a new organization for the protection of elephants or spotted owls pops up.
A more biologically accurate division (which I concede we ought to make for convenience's sake) should be according to sentience.
So after that long-winded spiel, back to Wootah's question: My answer to that is no, it is neither moral OR necessary to give 'animals' the same rights as humans.
But instead of rejecting any ideas or attempts to promote the welfare of our nonhuman companions (and enemies) because of a mythic creation story where man is conveniently given eminent domain over all other life forms, why not engage our critical thinking with modern scientific observation of animal behavior?
The atrocities caused by the Abrahamic religious line between humans and all-the-rest included feeling just fine selling a slaves children right out of her arms in the American south. That religious line in the sand is unspeakably evil when taken to it's literal extremes.