There is one inherent floor in the stop,start system, which is car batteries don't like to deep cycle, delivering huge jolts of power then being allowed to replenish, is what keeps them happy, in this respect they differ in design from something like a leisure battery which looks the same externally but is designed to deliver low currents for long periods of time essentially the internal structure is the same lead and acid but the design of the lead plates differed greatly to allow long deep cycling then charging repeatedly without loss of the plates surface to sulfation.
With stop start you need a regular car battery to deliver the jolt to start the car then when the car is in its stopped mode the battery is being used like a leisure battery to run fans ecus screen/mirror heaters radios etc etc, effectively deep cycling the battery.
Car batteries will charge quickly because of there internal design just as they can deliver power quickly, a leisure battery delivers the power slowly and as such will charge slower even if charged at the same current and voltage.
Stop start batteries fall somewhere in between but err more towards a regular car battery which means when stopped the battery really isn't happy.
Car alternators are designed to run the electronics on car and top up the battery but they are not battery chargers so they are not designed to deliver constant high levels of driven current to a battery, so to charge a battery you need to overcome its internal resistance and then push more current in, a bench battery charger will do this with ease as its designed to take your mains 240v 13A supply and push energy into the battery at 4+ amps continuously for long periods.
An alternator is pushing out current at 14ish volts but the current can be going up and down dependent on what is using that power and only a small amount is trickling into the battery. The steering on these cars can uses in excess of 90Amps so when this happens it drains everything the alternator can deliver and the battery gets abused as well.
So you have a battery which charges slower yet is getting used more to keep starting the car. When it's stopped the battery is being deep cycled in a way it doesn't like.
This is why it never hurts to give a battery a proper charge every now and again off the car. And why they don't last as long in stop start use.
Fiat basically bolted the stop start system into existing technology so the cars use a regular starter motor and a regular alternator.
Better systems use a combined uprated generator/alternator which is also used as a motor to spin the engine up. This system uses less fuel to start the car because it doesn't need to pour fuel in to get ignition it can slowly drip the fuel in till it fires as the motor is more than powerful enough to turn the engine at full speed. This type of starter is also better suited to a deep cycling battery so the battery can be more designed like a leisure battery for longevity and long power delivery, better for when the car is stopped, and the alternator/generator is designed to deliver much higher currents to properly charge the battery when the car is running.
If you are still with me, In answer to an earlier question fiat batteries are not 'crap' fiat stop start systems are crap.
I've seen it in the past but can't for the life me remember, there used to be a car that when stationary in traffic would change Mpg to Litre per hour, so you could see in realtime what the engine was doing, my old mondeo used to have a hidden test function that would also bring up this figure. I'm sure
MultiEcuScan would bring up this data if you wanted it to, it would be fairly simple to try it with a normal battery that's been used every day, then give it a good charge before trying again and seeing if there was much difference in consumption at idle, I would think that only if the battery is really depleted would you see the engine needing to use more fuel at idle otherwise it might not be normally measurable.
Just changing the temperature of the battery will change how well it charges.
So essentially stop start was designed to reduce co2 at the tail pipe, as pointed out once in regular use the benefits of the system become outweighed by the constant need to inefficiently charge the battery. But at least it looked good on the MPG tests and makes for a sales point 'this stop start thing will save you fuel'
I remember seeing it on a VW golf about 20 years ago on BBC's tomorrow's world so it's not new technology just with ever more stringent regulations on emissions it's working in the favour of the manufactures now.
As maxi pointed out though and I completely agree an older car 3-4 years old will be more efficient than a brand new car as the engine will have loosened up and worn in on the older car. So figures from fuelly don't really prove anything.