I'm not a copyright lawyer but it seems to me the Phillies have the stronger case. The company voluntarily gave up all their rights in 1984, and terminating the existing agreement requires the courts to view the company as the Phanatic's true "creator." IMO that just does not seem to be true, they were hired by the Phillies to execute something that is the Phillies idea, just as surely as whoever designs the team's logos and uniforms.
That doesn't mean they don't deserve to get a lot more $ given how valuable the character has turned out to be compared to what it was in 1979. But it does mean they will settle. The Phillies will be motivated to settle too, but they are the ones with the money and power to make it a long legal fight if not.