That's a big difference, with "inbox zero" requiring an email client with great archiving that works over multiple device types. Meanwhile, at the other end of the spectrum, the personal information managers need something more like Microsoft Outlook, with excellent search capabilities as well as a good storage contract on the hosting side because these types of inboxes are often tens of gigabytes (GB) per user.
An example here is the rapidly growing trend of "inbox zero." It's actually known by a variety of names, but it refers to the practice of keeping your email inbox count at zero stored emails. Essentially, it's dealing with every email as it comes in and then deleting or archiving each one so that your inbox is always empty. This boils down to a fundamental shift in how users are utilizing their email inboxes.