By playing the game on the medium difficulty you'll be able to play a final extra mission at the end of the game that is not accessibile on the easy difficulty. In the mission you must kill the T-Rex to beat it.
By playing the game on the hard difficulty you'll have to first defeat the T-Rex in the mission mentioned above, then you must play another final mission not accesibile on the other difficulties. You must escape the island in a helicopter while trying to shoot down another helicopter.
After comlpeting the fourth emergency mission a new weapon is aquired. It is a non-lethal weapon and is much more powerful than the Tranq. bazooka, but it comes with no ammunition and is loaded one shot at a time.