from a paper on evolution i wrote a while back.
Abstract thought. This is expressed in the ability of intelligent
speech. True, animals can communicate and have intelligence but it is
only a "practical intelligence". They are not able to think
abstractly, to hold a thought, ponder it and deliberate on it
abstractly. It is because of this that one cannot have an intelligent
conversation with animals, not even in sign language. Sure you can
communicate a bit but you cannot have an intelligent communication
like with a human personality. You cannot ask him what he did
yesterday, what does he think about this or that, for that requires a
higher level of intelligence, an intelligent personality - and this
animals do not have.
The consequence of this is something called free will. Free will does
not mean the ability to make decisions. Animals can also do that. Free
will means the ability to make moral decisions. For example, the
animal wants to eat, sleep, kick - and does it. So too, a man wants to
eat, sleep, etc. and does it. But man's free will is that he has the
ability to refrain from doing what he wants. To refrain from what his
nature wants him to do. This is the difference (Rabbi Matityahu
Solomon Matnas Chelko commentary to shaar bitachon). The animal is for
the most part compelled by its nature. Man has the ability to rise
above his base nature and act morally against the wishes of his lower,
animal self. This is free will. Animals have a form of intelligence
but man alone can be rational and deduce his moral obligations. Man
can hold a thought, contemplate it, analyze it and make a thought-out
decision. Man has an abstract thought intelligence, while animals only
have a practical intelligence. Therefore they are essentially ruled
over by passion and instinct. Theoretically, one can predict
everything that an animal will do throughout its life. An animal is
basically a machine. While for a man it is impossible to predict what
he will do. He himself does not know what he will choose. Therefore
man is a rational creature while animals are irrational. (1)
another source:
"When G'd created man, it says (Bereishis 2:7): "And man became a
living being." The Targum Onkelus translates this to mean that man
became a "speaking spirit". The human being is unique in all of
Creation as the only creature that can communicate through intelligent
speech" (2)
If you are looking for a difference in composition, see shaarei kedusha which explains the extra soul components of man over animals.