It not ment to make a difference in running but a difference in how quickly it gets up to temperature.
With the restrictor (well, technically a bypass valve as it does have a mechanical action) the engine warms up faster so the emissions stuff can start working more effectively sooner. (ok, so mabe it does make a difference in running as it gets it out of warmup mode quicker and onto the sensors and ECU sooner, but it's not actually something you'd feel one way or the other)
The mechanical action is such that when the T-stat is cold/closed, the spring loaded plate in the restrictor backs up from the coolant flow pressure and feeds most of the engine warmed coolant back through the water pump instead of the radiator.
Once the T-stat opens from coolant heat and pressure on the bypass valve drops, the spring pushes the valve back *closed and the coolant curculates through the T-stat and radiator in the more conventional understanding of coolant flow.
* It never truly completely restricts/closes off as it does have that small hole in the valve.