The only real difference is that in the like/likes of, the role of like is as a noun, whereas the normal usage is as a preposition or conjunction. See the Cambridge Dictionary for definitions.
I have never met a person like her before - preposition
I have never met the like of her before - noun
You can see that like is a noun in the second sentence by comparing it to this sentence:
I have never seen the portrait of her father
In both cases, the X of Y is the object of see, so it is a noun phrase.
Note that the singular like or plural likes can be used: as this Ngram shows, the singular has been in decline for a long time, but the plural form has enjoyed a rapid increase in popularity since 1970 in both BrE and AmE.
The expression does not have any intrinsic emotional tone, and can be used in a negative or positive way: the context indicates (or deliberately conceals) the intended meaning. It is generally used as a more literary or dramatic form of expression.