We're not animals. I'm so sick of people saying that, because we're an entire species apart from animals (which are a lower life form). How many buildings do you think would be designed by cats and dogs? ZERO. How many clothes do you think would be designed by ducks and chickens? ZERO. Declaring a human being an animal by process of elimination is like declaring an alien is a human because both species share arms and legs.
A lot of people classify themselves as animals while using deductive reasoning that since we're not from the "plant kingdom" or the "mineral kingdom", we're from the "animal kingdom". I don't buy it. Animals live off of instinct; it's "kill or be killed". They kill for food... they kill over territory... they killl because they HAVE to. Human beings are sentient, ordered beings with a innate moral fabric who don't HAVE to kill to survive. They kill for sport or because they're psychopathic. Period.
But to answer your question (if I were to ignore what I just wrote)... we certainly aren't the most powerful animal. There are animals that are way bigger, way stronger and way more vicious than we human beings are. As for your other question... I don't believe animals think, "Hey, we're the biggest and toughest on this turf, so don't mess with us!" They think on instinct, so it would be more like, "Hey, I eat little things like you for breakfast... run away before I pounce on you!" They don't think rationally. So no, animals don't think highly of themselves. Human beings do, however.