Ilford XP2 Super looks to the eye like a conventional B&W film -- it's got a clear (actually slightly purple) base color, not the orange color of most C-41 films. XP2 Super prints well on conventional B&W paper, in my experience. I've never tried printing it on color (RA-4) paper.
Kodak's C-41 B&W films, by contrast, have the orange mask that's typical of C-41 films. In my experience, it also prints fine on B&W paper, but often requires a higher contrast grade than is required for conventional B&W film, at least when printing on VC paper. (I find that it usually works best with effective grades in the 2-4 range.) Some people say they don't like the results of this combination (Kodak's C-41 B&W film on conventional B&W paper), but I haven't seen much in the way of clear descriptions of what's wrong with the combination, aside from insufficient contrast. This flaw could indicate differences in exposure or processing, different contrast preferences, differences in papers, or differences in enlargers between me and those who are more "down" on this combination.
I've done one 8x10-inch side-by-side test print to compare conventional B&W and RA-4 color papers with a Kodak C-41 B&W film. I didn't get an exact color match, so that was the most obvious difference between the two prints. The RA-4 print seemed to show a bit more fine detail, but that could have been due to slightly off focus on the B&W print. Because of this difference in fine detail, I slightly preferred the RA-4 print, ignoring its slight color cast. My sister, who compared the prints without knowing how they were printed, also preferred the RA-4 print. In practice, the extra hassle of getting the color right and working in total darkness mean that I generally print this type of film on conventional B&W paper. If I had some truly spectacular image on this type of film, I might try printing it both ways and keep whichever I preferred.
As a side note, you can of course print even conventional B&W negatives on color RA-4 paper. The main reason I can think of to do this is to get color effects without toning.