Which of them is the most effective/efficient (fuel?) way to make a supercharger use as little power as possible when not needed (say, cruising around)?
Not much up on clutched blowers, but I would imagine that the blower would have to be bypassed when the clutch is disengaged. A blower that's not turning would be a big restriction to airflow. A vacuum operated adjustable bypass would have to be the least complex to setup/maintain.
You got to realize what a by-pass valve really is and the purpose for them.
By-pass also known as a surge valve, is there to help the excess air that the supercharger compressor is producing from going back into the supercharger causing damage to the unit itself.
When you let off the gas your throttle body closes and the air that the supercharger is pushing has no where to go. The by-pass valve lets this excess air out so that it does not go back into the supercharger causing it to serge and causing the internal parts like the gears and other internal parts to get damaged.
So these by-pass valves is not really there to control boost levels, it is there so that you do not cause harm to the blower itself.
So, it would be similar to a CBV in a turbo. But, I could swear once I read something from Eaton they were claiming that it was used to help save fuel; I guess it was done by make it cutting down the work done by the supercharger using the bypass thingie.
Yes, Eaton does make that claim because the supercharger is always producing air and is always forcing air into the engine. And the way Eaton has their bypass, it actually vents around 1psi of boost into the engine when you are driving around normal. This 1psi allows your engine to not work as hard to produce power, thus leading to a fuel economy increase.