I've been using Inbox at El Goog for a while now, and I am happy to answer questions (in between dealing with a newborn...)
FWIW, I really like it, and use it exclusively for my work and personal accounts. Inbox functions very much more like a ToDo list than it does an email client. Here are the workflows I have:
Work:
I filter all mailing lists into different clusters that I have appear at 7AM every morning. I then scrub through the subject lists to see what happened yesterday, pinning things that require my attention, and then sweeping the rest. At this point, everything pinned in my Inbox is now "something I need to look at". I then read the email, and decide if it has an action item or not. If it's actionable and I intend to do it today, I'll leave it pinned. If it's not something I'm going to do today, I'll Snooze it until I think I'll have time to do it, or at least evaluate another Snooze time.
To make sure I don't miss important emails, I have a cluster that I put all email that has myself explicitly in the To: line, and have that appear whenever anything arrives. I do occasionally miss things that didn't have me in the To: and went to my 7AM clusters, but this is few and far between, and I hazard happens less than my Gmail inbox where I had far more cognitive load on managing the emails there.
Home:
The defaults are tuned well for home, and I use the clusters (like Travel, Purchases etc) like I do for work, having them appear at 7AM each day. Most things get swept immediately, and again I pin things that require my attention and are maybe ToDo items.
Inbox is really opinionated about its workflow: if you struggle against it, you'll have a bad time, and you'll prefer Gmail's flexibility. However, if you are Inbox Zero or GTD minded, I think you'll love Inbox. Inbox is my ToDo list, and replaces Wunderlist/Things/Evernote/Google Tasks for me. I set reminders to myself for work items that don't have an email attached.
I encourage everyone to give it a week to see if it suits them, but I'm afraid I'm all out of invites for now :(