I think Cole and Evil Cole would be a weird rivalry
Because Cole is the same person from different viewpoints
at no point has he ever had to struggle with his identity, he's either very good or incredibly bad
there were never any internal struggle for dominance. If you're good Cole, evil Cole doesn't exist and vice versa
Kratos vs Sweet Tooth
Whats the reason behind this rivalry? Nariko vs Kratos would've been better. Sweet Tooth vs Big Daddy with Sweet Tooth trying to abduct a Little Sister would have made sense and would've sparked a vicious and bloody rivalry easy.
Apparently its almost anything involving Sackboy.
EVERYONE CONFIRMED FOR SACKBOY'S RIVAL