Some reasons for using graded paper instead of VC:
Graded papers resond differently to pyro negatives (or other negatives developed with staining developers). The stain on these negs are some shade of yellow/brown and block proportionally more blue light, thereby increasing contrast, especially in the highlights where separation can be difficult. VC papers have the opposite response, since more green (low contrast) light makes it throught these areas than blue (hard contrast) light. (This could be useful for reducing contrast in the highlights, but this is rarely necessary).
There is some concern about sharpness in VC papers due to the different focus of the different colors to which the paper is sensitive to. See Ctein's book for more on this.
Graded papers do many times respond to toning better. This, however is a question of formulation and could be controlled by the manufacturer. Also, VC papers have a tendency to split-tone more than graded ones, something some of us find undesirable.
Dealing with filters is a hassle and usually increases exposure time. (Most users of graded paper tailor their negs to one contrast anyway. Although this is not foolproof, we graded paper users are usually in the ballpark and need only go one contrast grade in either direction to get a fine print.) Intermediate contrast is achieved by manipulating print developers or switching brands of paper.
Some reasons to use VC paper:
Split-contrast printing! You just can't do this with graded paper. (That said, I use graded paper almost exclusively and rarely miss this possibility.)
Less paper hanging around "in stock".