One thing that bugged me slightly while reading about the Mahabharata was this idea that "lower" animals don't have sentience or something. For a religion that believes in reincarnation, how is that even an idea?
There is sure a difference. Though animals too have their social norms, they do not have the capacity to do evil or good like we have. I do not know which portion of Mahabharata are you referring to, but this greater thinking capacity has put us under greater responsibility, more obligations towards our fellow humans and other who share this earth with us.
Hindus consider that to be born as humans is a chance for spiritual development and for believers an opportunity to attain 'moksha', 'nirvana', release from the cycle of birth and death and reach the God-head which must not be missed. This theme is constant and strong in our religious poetry.
"Tune raat gawayi soye ke, diwas gawaya khaye ke;
heera janam amol tha kaudi badle jaayen." - Kabir
You wasted the night in sleeping, the day in eating;
your birth was a precious jewel, you are trading that for cowries.
* Traded just for eating, sleeping and other mundane things and not making any spiritual progress.