Personally, I eschew utilization of an over-augmented, trisyllabic linguistic unit like "cognizant" to express a paradigm when diminutive constructions are accessible.
I applaud you for NOT asking, "As 'cognizant' is longer and sounds more intellectual than 'aware' while it means pretty much the same thing, is there ever a time when I should use 'aware' when I could say 'cognizant' instead and sound so much smarter?"
On the serious side, I think the only time I've used "cognizant" was when I was doing contracts for the military and the word had a specialized technical meaning: a "cognizant activity" was the agency or department responsbile for some contract or task.
While a simple dictionary definition doesn't make this distinction, to my mind "cognizant" implies a true knowledge about or understanding of something, as opposed to simply having heard that it exists. So "Bob is aware of calculus" says to me that he knows it exists. "Bob is cognizant of calculus" tells me that he really knows something about it.
You might use "cognizant" for the same reasons that you would use any synonym: to avoid using the same word several times in the same sentence, to avoid unintended rhyme, to avoid using a word that sounds too similar to another word you have just used, etc. For example, if I started to write, "Are you aware that Wally is aware of the need to be wary of Warren's ward's housewares?", I think I would start looking for alternative words, and replacing one of the "aware"s with "cognizant" would be a possibility.