It's hard to imagine these first person shooters are better for faster thinking than a good racing game or speedy puzzle game. Super puzzle fighter 2 turbo, anyone?
I'm thinking that "the violent games that often worry parents most" is a code-phrase for the Grand Theft Auto franchise, which is not, strictly speaking, an FPS.
And the difference between a GTA game and a racing game is one has you racing around on a track, and the other has you racing around in a city, navigating traffic and obstacles while being shot at by helicopters. One has the objective of "go fast" while the other has the objective of "go fast while avoiding committing other crimes that will escalate the law enforcement response even further, and while navigating to a spray-paint shop which you may or may not have already located on the map in advance."
So for the purposes of this comparison, GTA equals more challenges, more objects and objectives to keep track of, more decisions to be made, and therefore, more cognitive benefit.
My DD plays a game inspired by GTA called "The Simpsons - Hit and Run," which incorporates a lot of the best elements of GTA but reduces the violence to a cartoon level and subtracts the gunplay. I've showed the game to a number of nieces and nephews, and I've yet to find a kid that doesn't love it.
