In Pathfinder
Perhaps because the Blood War isn't OGL-covered,
Pathfinder makes no use of it. Demons and devils fight, yeah, but that's because they're
evil, destructive bastards who sometimes get in each other's way. There's no big philosophical fight between the two. Indeed, as demons in Pathfinder are created from mortal sins, and devils live to corrupt mortals by committing sins, one can say that devils literally
create demons.
This does not explain why, since the demons have vastly larger numbers than devils, same as in D&D if not more-so (The Great Beyond cosmology doesn't go into the whole 'balance' thing), they didn't destroy much of Golarion and the Prime Material Plane already, given how none of the Celestial races focuses on directly opposing them, though local gods are known to. In fact, demons and devils so rarely come up against each other in Pathfinder Adventures/Modules, that it often feels like Paizo is trying their darnedest to not even hint at there being something similar to the Blood War in their universe, and get sued by WOTC.