Kratos Vs. Nariko
Kratos and Nariko would not be a rivalry, more like a love at first sight
You know, I'll make a wild guess and say Big Daddy's rival would be Sweet Tooth. Sweet Tooth could be just blood-thirsty enough to go after Little Sister for no reason, making Big Daddy fend him off.
Though I got this impression that the rivalries wouldn't be same in vice versa, so Sweet Tooth's rival could be someone else. And since I've heard that SB have made some rivalries based on little fun facts (Dante vs Nariko because of Ninja Theory), Drake vs Sweet Tooth could very well be possible, based on Drake's fear of clowns
soo far we have
here are some of my rivalries i would like to see or wish were in the game.
dante/sir dan (sir dan is undead and to my knowledge doesnt dante kill creatures like undead already? i think it would fit)
sly cooper/drake (the thief versuses the treasure hunter, where drake find something in which sly wants to take)
fat princess/sweet tooth (fat princess mistakes sweet tooth for liking sweets like ice cream and cake instead of craving murder)