“Old” call of duty is based from WWII, which were made in the early 2000s inspired by Medal of Honor while “New” call of duty is the fictionalized takes within the FPS genre (basically the ones you recognize today). Modern Warfare (the 2007 one) is the title that departed from the WWII genre while World at War tackled at both theaters of WWII (the Pacific and European).
So your question is not about the games itself, if they are better games, but what style of game world you prefer. I personally was never a fan of the old realistic World War styled games (Medal of Honor, Call of Duty, Battlefield). I prefer Modern Warfare and Black Ops or one of my favorites, Titanfall. That does not mean the old games are worse, its just I do like the newer styled game worlds more.
I understand that some people want a grounded and more realistic, almost simulation like experiences of real world war scenery. There are even games focusing on that, at least on PC, like ARMA 3 or the new ARMA Reforger.