I tried Mailbox shortly after they were bought by Dropbox. Lovely app with a nice UI. Unfortunately, it solves a problem I don’t have. If I’m not going to deal with an email right away, I send it to Omnifocus. Mailbox doesn’t offer much if you’re not using the “save for later” feature.
There were also a couple of things I just didn’t like. The push notifications have less information than those that come to the built in Mail app. Mailbox gives you the sender and the subject, Mail also gives you the first line of the email. And with Mail, the email is there as soon as you open the app. Mailbox has to download the mail after you’ve launched it, so there’s a small delay.