I must say, after some playing around, I am liking the Share to Classroom extension better and not because Google made it. It has an amazing push to class feature that the other extension does not have.
Push to Class/Teacher - This is AMAZING
Teachers can push websites directly out to students (students must have the Chrome extension downloaded and enabled for this feature to work) and it will automatically open up in the students Chrome browser. This is great for wanting to share a resource with the students all at once, but not necessarily put it into Classroom. After some testing, I did discover that students do not need to be logged into computer at the time of the push to receive the resource. They can retrieve it when they login.
On the flip side, the students have a push feature on their Share to Classroom extension, but they can only push resources to the teacher and not other students. When the student pushes a web resource to the teacher it doesn't automatically open in Chrome, so the teacher must go and retrieve it.
From the student perspective:
Locate 'pushed' resources:
Make Announcement/Create Assignment
This is similar to making announcements or creating assignments in Classroom. The only catch with the extension is that you can only post to one classroom at a time. To work around this, you can save it as a draft, open it up in Classroom and then assign to multiple classes at once.
I think this Chrome extension is definitely worth a try!