I decided to out things in perspective a bit and suggest some rivalries for a PSABR sequel (If there will be one)
I decided to start with Sly, now there is the possibility that they could keep the old rivalries and only give new ones to the new characters, but what's the fun in that?
Nathan Drake (His old rival)
Billy Kane: King of Fighters/Fatal Fury (Billy is a criminal, but only steals because he can't afford. I could see Sly insulting his methods after Billy tries to steal from Sly)
Garret: Thief (This is a given, Thief vs Thief)
Goemon Ishikawa (Samurai Warriors) They are both thieves XD
Ezio (Suggested by someone on Facebook)
If you have anymore rivalry ideas for Sly feel free to share them with me