I’m going to say it but overall when you compare every aspect that makes a top international bowler than I think Anderson is the better of the two.
Like it or not both Cook and Anderson are world class international players. Would they make it into an all time test team for some yes and others no but in there current career periods both are Legends and both will finish there career as in the top 5 or 10 ever in the history of the game so by definition a cricketing Legend.
Quantity over quality for both Cook and more so Anderson. Without the Duke ball, Anderson is average at best. Disappears in most overseas series. World class and great of the game are two totally different kettle of fish. Just because you score more than another doesn't make you the better player.
Shearer scored more PL goals than Henry, does that mean shearer is better than Henry? Most certainly not.
Bill Russell is an 11 time NBA champion, is he better than Michael Jordan? Again certainly not.
Schumacher has more wins and championships than Senna, again is Schumacher better than Senna? Not in a month of Sundays