What is missing about the statement is the human aspect. A chimp may use a tool, such as a stick to collect ants, or a rock to smash a tough fruit. The human mind is capable of much more.
The human mind is capable of flight, both airplane and to the moon. The human mind has brought us to the ocean depths. The human mind can examine the world at large, such as a super telescope to explore the universe, or on a microscopic scale, exploring atoms and single cells.
The human mind produces creativity. Not just cave paintings and drum circles, but masterpiece paintings, archetecture and a symphony orchestra.
We imagine, we wonder, we plan, we predict. All of this goes on, and you wonder how one could call are brains 'tiny'.
Yet despite all this, we ARE animals by nature. Our basic drives are survival, food and sex. We are territiorial, and will often fight before we debate. Get us in a group, you will see pack (mob) mentallity. Run us through some basic tests, and our reactions will be not much different from that ape.
A religious person might take offense to the original question and say we are divine in creation, and to imply we are apes is an offense to god. A scientific person might explain the marvels of evolution, and although he couldn't tell you why we are so much different than an ape, he could quantify the differences.
On the otherhand, a skeptic and moderate such as myself, would tell you this... Mankind is more than an animal, yet not much more. We are capable of wonderful things, but we must remind ourselves of our primitave roots and instinctual nature, because if we forget, it is easy to regress to it.