Call of Duty: Modern Warfare and Warzone currently run in backwards compatibility on both PlayStation 5 and Xbox Series X. While the Xbox Series X version did recently receive support for 120 frames per second, the PS5 version is still locked at 60 frames. That however might be on the verge of change.
According to a post on Reddit earlier today, the new Sony console briefly listed a PS5 version of Modern Warfare which would presumably include Warzone as well. Neither Activision nor Sony Interactive Entertainment has confirmed any such upgrade at the time of writing.
Call of Duty: Black Ops Cold War is already making use of the new consoles by featuring enhanced visuals and better frame-rates. That is in addition to the integration of DualSense features on PS5. The preceding Modern Warfare should hence also receive the same treatment with a proper next-generation upgrade.
Not to mention that Black Ops Cold War will be supporting Warzone and which will likely be when the new PS5 and Xbox Series X versions are announced.
Activision has confirmed that Black Ops Cold War will be integrated into Warzone in early December alongside the release of the first battle pass. This will allow players to use their Black Ops Cold War weapons and operators as well as cosmetics while also accessing the older Modern Warfare content in Warzone. Modern Warfare, as well as Warzone, should receive PS5 and Xbox Series X versions in the same window.
PlayStation 5 and Xbox Series X owners should be cautious when deciding between which of the two Call of Duty games to install. Black Ops Cold War requires at least 250GB of storage space on PC for the complete experience and for players who want to play in glorious 4K resolution with ray tracing and ultra settings enabled. Modern Warfare has similar requirements when adding up the storage space needed for Warzone.