That Mophie case definitely looks a lot bulkier than the Apple Battery case. The mophie case looks like something I would bring along on an extended camping trip where I know I will have no ready access to power, but not something I would like for normal everyday use.
The primary reason why I never considered using a Mophie case on my 4s or 5s was primarily because I felt it looked like crap.
The Apple battery case seems to be the reverse here. The battery life it offers is less, and that's fine because it should still prove sufficient for someone to last their iPhone through a normal day. You are likely looking at someone whose iPhone 6 is probably at 20% by 4 pm, and the case should let them extend that till at night, just nice for a recharge. Between the two, the Apple case would probably fit into my pants pocket a lot easier than a Mophie case, and I would have less qualms about walking around with the former in my pocket all day.
I think it is safe to conclude that the people Apple is trying to attract here are not die-hard Mophie fans, and focusing strictly on specs like "extra battery life" tells only one very lopsided part of the story.