Both are pretty much the same. The main difference is that 'greedy' is more of a selfish desire of something.
Rapacious: 1) excessively grasping or covetous. 2) living on prey 3) very eager or greedy for food, satisfaction, or gratification.
Greedy: 1) having a strong desire for food or drink . 2) having or showing a selfish desire for wealth and possessions.
You can see that the only difference is the word 'Selfish' which makes it more of a negative word to use. However, animals like coyotes, foxes, and bobcats can be Rapacious because they live on prey.