I'm going to sum it up like this: If you want Zombies, play Cold War. If you want a great multiplayer or campaign experience, stick with 2019's Modern Warfare. Seriously, Cold War took two steps back from the advancements MW had made towards revitalizing the series. It was developed on an older engine, retains the earlier games "Cartoony" art style, lacks the mount mechanic that MW perfected, and is an overall watered down experience. You will have significantly more fun playing the multiplayer modes offered by Modern Warefare, like Gun Fight and traditional TDM, than on Cold War.
Another downside is that the developers, Treyarch and Raven, have gotten lazy with Warzone, which they inherited from MW. Rather than revitalizing the game for the launch of Cold War, they waited 6 months to drop a "new" map, which is almost exactly a rehash of the old map, with some changes to points of interest. Pretty sad.
Hopefully Treyarch and Raven are benched next time they're up to make a CoD game, and it sticks with Infinity Ward or Sledgehammer.