As far as I know, there's no canon information detailing the differences in the books (I could have forgotten something). I suspect that's just a throwaway line intended for slightly humourous effect (a girl in boy's clothing!), and also to indicate just how busy it was - Madame Malkin is so rushed off her feet that she can't even take time to look at her customers and determine whether they're male or female.
Regular school robes
Men and women tend to have different body shapes, especially after entering puberty. I'd suspect the difference - if there is one - in school robes would likely be in the cut to suitably fit those differing body shapes.
The quote says "dress robes" which are robes worn for formal occasions. Hogwarts students required dress robes for the Yule Ball in Harry's fourth year (the events of Goblet of Fire), and they likely would have also worn dress robes for Bill and Fleur's wedding (beginning of Deathly Hallows). In addition to reflecting the different body shapes, I'd imagine there may also be different patterns and colours for women's dress robes rather than men's.