Ilford's original XP1 chromogenic used a slightly modified C-41 process that resulted in higher densities and contrast than running it through the local C-41 lab. Ilford sold XP-1 processing kits in at least a couple sizes for home and small-lab use, containing very C-41-like chemical solutions but which specified 5 minutes development (as I recall) instead of C-41's 3.25 minutes at 100 degF. The standard lab C-41 worked ok too, just with slightly flatter negs. This wasn't all bad, as at least it recorded a wide range of scene brightness, but usually called for higher-contrast printing paper. I did a lot of my own XP1 film processing, and printed a lot on Ilford Multigrade papers.
There was no corresponding XP2 processing kits, I think, when the improved chromogenic was introduced. I'm certain that one of the improvements was to make the film more fully compatible with the standard C-41 process, with normal negative density and contrast. The old XP1 processing kit still worked, as it did also for Kodacolor II.
I don't know if it's true, but back in the XP1 days we were told that the film did have three dye layers like color films, just that the dyes were all black, and that the layers aided the claims of wide ISO tolerance. If so, then this would also support the idea that the chromogenics have some inherent advantages over color neg films printed as B&W, say in tonal qualities. This is CERTAINLY true in the conventional darkroom printing on B&W papers, especially multi-contrast ones, since Ilford's, Fuji's, and Agfa's chromogenic films had no orange mask to mess up the effort.
Scanning removes the masking distinction I think, and post-processing might well address other differences. Still, I happily use Ilford XP2 and its Fuji clone (giving generous exposure), and like the "look".