Giat 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.
I suspect you mean a combined starter and alternator/generator. The system that Fiat has used is just fine for regular ICE engines that don't have any sort of hybrid drive.
The reason why a alternator never does as good as a battery charger is that in a stop/start application it gets interrupted, has some of it's current drained for use on lighting,radio, steering etc etc whereas a battery left overnight is doing nothing but charging.