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.
It seems to me that GTA games don't offer the challenge of perfection. With a racing game, you may be inclined to achieve the fastest possible time on a track with a given vehicle, and "go fast" actually implies the following: modulate the throttle or brake perfectly at every given moment for the duration of the race. Be in the right gear at all times (dependent on speed and engine power curves). Follow the ideal line, setting up for the entrance to every new turn when exiting the previous. Maintain the maximum amount of speed over elevation changes while keeping the suspension loaded in order to maintain control (unless the it's OK to take air, in which case you still have to take the "right" amount of air). When you seek perfection, you are forced to consider a number of subtleties that you can otherwise ignore. I think a good racer is constantly considering things that are probably not even included in the physics model of games like GTA. In short, I think racing is as complicated as the driver (gamer) wants it to be. For you it may be simple, probably because your interests lie elsewhere.
Additionally, you can race online against other people to add an unpredictable element to your experience.
