I liked Mailbox but Dropbox own it and I'm more and more concerned about how they handle my privacy. Add to that that for Mailbox to work your emails have to be stored on their servers (AFAIK, please tell me if I'm wrong) I switched away.
Only the snoozed mails are stored until they are redelivered, as far as I can tell, but I can see your point. I personally don't care that much about privacy, if the convenience gains are high enough :)
"Mailbox stores a subset of your emails temporarily in order to redeliver snoozed emails, provide fast delivery and provide push notifications. We encrypt all communication to and from the Mailbox app, and all information cached on our servers is stored in an encrypted format." [0]
Dropbox directly lied to users about privacy and stated they could not access your data. When this was pointed out, they made up excuses for lying and acted rather snotty about it (on HN). They also had that little "don't check passwords" incident, which night indicate more serious problems. I'd trust Google engineering over Dropbox, but Google is also evilly anti privacy so it's not much of a win.
Google already has my emails (Gmail). If I use Mailbox I'm throwing another party into the mix. Google continues to get them and now Dropbox gets some of them too. It would be best to use the service of the company that gets them either way (Google). Why give your email to two companies when you can give them to one and get the same features?
