I may be wrong but I don't attend the school of thought that thinks that animals have a "6th sense" .
As Spiritalk mentioned, they live by their instincts and yes they have senses that we , as humans, need to learn from them and how they use it so well for their survivals and many other worthy purposes.
They have psychic senses most definitely if that's what you meant VN Purohit, which enables them to do many things that we , as humans, can only do when for example our clairvoyance opens or clearaudience or other psychic senses for that matters.
In that sense (no pun intended

) they are quite sensitive...
The cat ,for instance, is a remarquable animal in regards to psychic senses.
I would go with what Spiritalk as to us developing our psychic senses with Free will which is not the case for animals and humans having free will can use it for ill or for Good depending on one's intentions.
You will never witness a normal animal, however wild, use their abilities to cause deliberate harm or to use that for another function than to follow their instincts.