Mailbox is kind of a special case. Like I said above it acts as a "man in the middle", downloading all your email and saving it on a server in their datacenter, performing manipulation for filtering and priority, then shipping it off to your phone. Thing is, it's completely free to download and use. So it incurs significant costs but generates no revenue whatsoever. There are no ads, no in-app purchases, and they promised not to mine your email. And that's why Dropbox is killing it.
Carousel was developed by Dropbox, from assets they acquired, so it's not a startup product. It's just a failed one, like Google Wave.