I've thought about this for awhile now...it doesnt seem likely that most third party publishers are going to allow their characters to be sold or even had for free in a pack with a competing game's character. I'm going to guess that either their 3rd party character will have to be paired with a Sony character, or they will have to allow for two characters from their stable to support the rivalry, etc.
A good example would be Activision; If we do get Crash he's not going to rival Ezio or some other third party character. The rivalry interaction would require permissions out the ying yang from both companies and would be a nightmare. Why do you think all 4 of the current 3rd party characters are rivaling Sony-owned characters?
I guess the plus side to this is that we could get two reps from a few of the companies, like Ezio or Connor + Rayman, Crash + Spyro, or Kiryu + Sonic. Seems unlikely, but it also seems highly unlikely Acti will allow Crash to share spotlight with a competitor character.
depends on the companies. for example, solid snake/old snake/big boss vs altair/ezio/connor would be easy. Why? Metal Gear Solid and Assassin's Creed have been taking friendly shots at each other for years. MGS4 had an unlockable altair costume. AC Brotherhood had an unlockable Raiden costume. And MGS Peace Walker made fun of the "leap of faith". I bet they'd be totally cool with a rivalry. But for the most part, yeah, i think it'd be extremely tough for companies to agree to this