Pretty sure on what I've read up on the Moment battery case is that it's going to be the equivalent of plugging your phone into a wall charger. It will not display the battery juice in the Battery Widget nor act as an extension of your current battery like the Smart Case does.
Your iPhone will know it is plugged into a Smart Battery Case so you will get those features, plus your phone remains in "mobile mode". In other words, when your phone is using the Smart Battery Case it won't immediately start doing battery intensive processes such as indexing or iCloud backups while connected to Wifi because it knows it is not plugged into a wall. If any other battery case (including the Moment case) is put on your iPhone and switched on, your iPhone will immediately think it is plugged into a wall and start processes like that.
I like to think of those battery cases as external charging. The Smart Battery Case I see as an extension of your already existing battery.