The skinny narrow tires in competitions are for reduced aero drag. They are also likely at pressures you don't want for every day driving. There is too slight of a difference here between the tires to really change this.
Contact patch size depends on the tire pressure, load weight, and tire design, in addition to tire size. Narrower tires do have a thinner contact patch, but the patch size also gets longer. There may not be much change in the area between them.
The change in revolutions per mile changes the effect final gear ratio, so the engine can work less per mile. Be sure to factor in the speedometer adjustment to the odometer reading to get the correct fuel economy results.
Some tire size calculators.
https://tiresize.com/comparison/
This one goes in depth.
BND TechSource - Tire Data Calculator