Obviously not, because there both dead.
Corythosaurus lived in western North America near the end of the Cretaceous. Its predators would have included Gorgosaurus and Daspletosaurus.
There is only one type of Tyrannosaurus rex. There were many different tyrannosaurs, dinosaurs related to Tyrannosaurus, including but not limited to Tarbosaurus, Neotyrannus, Albertosaurus, Gorgosaurus, and Daspletosaurus.
Gorgosaurus was created in 1914.
Daspletosaurus was created in 1970.
Daspletosaurus was a carnivore and usually preyed on Maisaura and Einiosaurus.
Tyrannosaurus rex belonged to the family Tyrannosauridae, which includes other large theropod dinosaurs like Gorgosaurus and Daspletosaurus. Within this family, T. rex is the most famous and well-known species due to its size and iconic status as a fearsome predator of the Late Cretaceous period.
The Daspletosaurus was a carnivore. It was a cousin of the Tyrannosaurus. It ate herbivores and some other smaller meat eaters.
gorgosaurus or albertosaurus
Albertosaurus, Daspletosaurus, Troodon, Quetzocoatlus
Tyrannosaurids (relatives of T-rex), such as Daspletosaurus and Gorgosaurus, almost certainly hunted Parasaurolophus. Dromaeosaurus, a raptor, may have been able to bring down large prey like Parasaurolophus. All kinds of small omnivorous and carnivores would have eaten Parasaurolophus eggs if given the chance. These include Struthiomimus, Saurornitholestes, Troodon, Dromaeosaurus, and many others.
Utahraptor, Arcrocanthosaurus, Gorgosaurus, Dromaeosaurus, Hallalikian and Noasaurus.
Tarbosaurus, Albertosaurus, Daspletosaurus, "Guanlong", Nanotyrannus, etc.