In short, the clutch in the fan allows the fan to spin at full speed when the motor speed is slow but as the RPMs rise, the clutch slips and allows the fan to spend slower than motor speed. Thus less drag on the motor when the speed of the car is providing extra air flow. A flex fan will just flatten out at higher RPMs.
A clutch fan in good condition should provide the same cooling as a fixed fan. It "clutches out" at higher rpm's. If you're cruising down the highway at 65 mph, what do you need a fan for? You've already got a 65mph air flow.
For a few extra dollars you can get a thermostatic (or heat-sensitive) clutch. Like when you start your car in 30 degree weather, what do you need the fan for?
They work pretty well. Watch out for the cheapos from Pep Boys and such. They sometimes start slipping after a couple of month's use. A slipping fan clutch is junk and WILL make your car overheat.
I doubt if you'll notice any significant difference in gas mileage, but they do save a little gas and every little bit helps. I like them, other than the above mentioned cheapos.