At work I've been running a very successful inbox zero for some time. Once an errand is taken care of it goes in the archive. If I need to remember something I move it to the todo list (currently using Wunderlist). At the moment this is working very well and I manage to handle most of the emails I get within a day or two.
But at home inbox zero really isn't working. I don't have the discipline to keep the inbox clean. I use it as a read later list, as a way to remember to answer people, buy things, pay things and so on.
Mailbox is extreamly new and I don't fully trust it to be bug free. Nor does it have a desktop app. For these reasons I haven't entrusted it with my work mail. Instead I've given it my private mail and its been doing a good job with keeping it clean.
So far I'm extreamly pleased with the app. It's simple, fast and smart and with some luck it will keep my inbox zero at home.