동물 is formal word. you can see it in dictionary with chinese character.

짐승 is not chinese character. It using by mouth to mouth during long time in korea.

So 짐승 have more emotional meaning. 

For example, Human is kind of 동물(animal). but not using 짐승 when explain human.

If you see someone called 짐승, then you can imagine someone hated.

ex) (화내면서) 짐승같은 놈!

But sometimes, woman saying 짐승 when she call someone who she like.  

ex) (웃으면서) 이 짐승~

Basically same

But we normally use 짐승 for big and danderous animals like wolves.