At the moment, they provide two very different views of email. Actually I guess you could say the old GMail client offers two different views itself, since it has both standard and priority inbox.
It's not clear that Inbox is the right way to look at email for the majority of users, and I'm saying that as a user/tester. I've had to drop back to the regular GMail app do do things a couple of times and Inbox has crashed twice on me.
Note that the GMail client did take on some of the look and feel such as the (+) widget on the bottom right.
The widget is the 'floating action button' in Material Design parlance. You're suppose to use it in screens which have a clear 'primary' purpose. In pretty much any email application, that'd be a compose email button from an inbox (or similar) view. So I guess in that particular case, it's not so much GMail taking from Inbox, so much as both of them are showcase material design apps, and Inbox just got released 'first'.
I love it, and really hope they continue to maintain both. Inbox works great for my personal email where each message actually corresponds to a task I need yo complete, gmail is a great workflow for my publicly visible work email where its more just a stream of messages, some of which need to be dealt with and others are just record keeping.
Inbox is for people who don't have a workflow / need help organizing their workflow. The app looks neat, but I already have my own workflow and it doesn't fit in it so that app is not for me.
I didn't really get it until I started managing emails in mass(or bundles if you want to use googles terms). I get a lot of email that isn't spam that I know at a glance if I need to read it or not. With Inbox I can really quickly archive a huge group of emails that I don't need.
I have also used the pin and reminder feature a few times. I still think it's a weird thing to include with email, but it was helpful.
I would have totally jumped to Inbox but it seems there is no way to mark an email as 'read' without having to actually open it. It's kind of flabbergasting and seems very limiting to me.
It definitely feels like a bit push for 'lock in' (not that gmail really needs that...).
If I am wrong, someone please tell me how to do so from a list view.
Also, from what I hear (I'm not allowed to use it yet), Inbox doesn't let you use labels like labels (multiple labels per message etc), but tries to enforce a "folder-like" view...
[A horrible mistake if it's true... Labels are a significant advantage of gmail over many other email clients.]
Ok, that's fine, but I have existing gmail filters that send 'promotions', automated emails, etc... far & away from the inbox. What's the plan with those?
Sometimes I like to peruse the ones that I've not yet acknowledge receipt of and either j/k + x to select the ones I want to dismiss outright, which I can still do in Inbox, and then shift-i/click mark as read to mark em my equivalent of 'done'...
The actions presented in Inbox will leave the 'unread' business to ever grow and clutter any IMAP connected application and searches like is:unread.
Edit: Maybe the more troubling aspect of the removal of the 'unread' handling is that these emails will certainly go unseen/missed which is bad.