What is the difference?

[seth.destructor]

What a nice girl!
What nice a girl!

[Gość: Steve]

The first means she is a pleasant person. The second might be intended to be "How nice, a girl" meaning that its good that she is a girl eg as a new person in a workplace previously full of men. The use of the exclamation mark may indicate irony ie she or it isn't liked.

[seth.destructor]

I've found a few examples in books, and surely it isn't "What nice,
a girl!" Maybe it is something like "What nice (kind of/sort of)
girl!"?

[Gość: Steve]

"What nice girl!" might be used to indicate that the person doesn't think there
are, or doesn't know any 'nice girls' (caring, family orientated, well-behaved,
etc). It would respond to something like "All the girls you've been out with are
bitches, its time you found a nice girl" or "Its time you stopped your wild
life, settled down and have children". Find yourself a nice girl."