So far, the next generation of consoles seem to be running the game in a fantastic way. In an article from Essentially Sports, the quality of Black Ops Cold War on next generation consoles is analyzed in some detail.
For both the Xbox Series X and the PlayStation 5, there are modes to run the game at 120 Frames Per Second and with Ray Tracing. It appears that both are fairly successfully running within the game.
Black Ops Cold War quality on Xbox Series X and PlayStation 5
Before any more praise is placed on how well Black Ops Cold War runs on next gen consoles, potential buyers should know that there are quite a few bugs that affect the next gen Black Ops Cold War.
When Black Ops Cold War was released for pre-order, there was a next gen upgrade for players to purchase in order to immediately have access on a new console. When downloading Black Ops Cold War on a new next gen console, there are different versions of the game to download.
It isn't clear why this is the case right now, and the next gen version isn't automatically downloaded. Even when the correct version is chosen for Black Ops Cold War, many reports have shown that the previous generation version is running and causing plenty of problems.
In some of the worst cases, the Xbox Series X is facing substantially more crashes with Black Ops Cold War when compared to PlayStation 5. There are even reports of the Xbox Series X being completely bricked and being unable to turn back on due to crashes from Black Ops Cold War. It's very likely that this is all causes by differing versions of the game and early bugs.
However, once bugs are fixed and some time has gone by, the outlook of how well the game runs on next gen consoles is promising. Both the Xbox Series X and the PlayStation 5 have the capability for 1080p resolution, 120 frames per second, and optional ray tracing. Those are all well worth the price of a next gen console.
The Xbox Series S doesn't have 120 fps or ray tracing ability, but the 60 fps is still possible, which is a large leap over previous gen hardware.