Having played shooters since the arena shooter days... no, I definitely disagree.

I like to compare arena shooters vs. Fortnite/Overwatch as chess vs. Settlers of Catan. Arena shooters were much more "open play" in the sense that there were few enough game mechanics that you could mostly guess your opponents' tactics and it often came down to execution and minute variations in the gameplay.

The newer shooters add many, many game mechanics that complicate and randomize the game. Overwatch's large stable of characters, for example. This creates a problem where part of your skill is reading matchups from an intractably large number of factors, then executing on it.

I don't consider either to be superior, but the games put emphasis on and reward different skills.