Both are correct, but in the first sentence the word 'whatever' must be followed by a word like 'person', 'child', 'woman', 'man' etc. The sentence is incomplete as it stands. Here are some examples of how to complete the sentence: They talk to whatever child/woman/person will listen OR They talk to whatever child/woman/artist is there.
The second sentence can stand on its own in informal speech, and needs nothing more to complete it.
There is no real difference in meaning between the two.