I should have mentioned that my experience with stop-start is only with manual transmission cars that start the engine upon touching the clutch, sometimes before it is in full contact and usually before I'm ready to release it. If I'm going for a fast start I start the engine preemptively by lightly touching and releasing the clutch.
The other commenter's frustration with automatic transmission vehicles that start the engine upon releasing the brake sounds valid to me, especially if there isn't a convenient way to start the engine preemptively.
I have used two cars with start/stop: Renault Megane and VW Polo. Both were diesels and had automatic transmission.
Both of them started the engine just before my foot leave the brake pedal. I think they sensed the rate I eased them and decided that I'm going to roll.
I also drive an automatic Focus as my daily driver which doesn't have start/stop and didn't have a noticeable difference in their driving experience during stops, TBH.
Maybe some cars have different implementations and algorithms. A brand had on demand stop IIRC. You pressed brake a little harder to command the car to stop the engine.
The other commenter's frustration with automatic transmission vehicles that start the engine upon releasing the brake sounds valid to me, especially if there isn't a convenient way to start the engine preemptively.