When Mailbox first came out, there was no Google Inbox, no snoozing, and the ios e-mail experience was lacking and sluggish in general. Mailbox fixed all that, and it was the first to properly do so that we trusted. We trusted it as it was by the well established Dropbox.

But since Inbox came out, I have seen no reason to open Mailbox, and I would say that Mailbox actually inspired Inbox.