Your comparison between Switchboard and Inbox is solid. Switchboard is being used for tasks like sending "new email" push notifications to mobile clients, or uploading attachments to dropbox. I haven't used Inbox yet, but I'm excited to try it out.

It's great that Inbox is also built on top of IMAP. The new Gmail API is great, but an application which takes advantage of it is locked into using only Gmail. By building from the standard, Switchboard and Inbox are cross-provider.