The new tool is at google.com/webmasters/tools/mobile-friendly and it basically gives you a pass or fail grade. Either it tells you that you are mobile friendly or you are not mobile friendly. The messages I was able to generate include:
In each output, the yes, you are mobile friendly or no you are not, Google may or may not give more or less advice depending on the site.
For example, for this site, we got an “Awesome! This page is mobile-friendly,” but it did add that “this page uses 9 resources which are blocked by robots.txt. The results and screenshot may be incorrect.” It then listed out those resources it had issues with, so you as the webmaster can decide if it is something that needs addressing.
Here is a screen shot:
Here is a site that seemed to get no additional feedback from the tool, outside that it is mobile friendly:
I then tested a site that I know what not mobile-friendly and Google explained what the issues were including (a) text too small to read, (b) mobile viewport not set and (c) links too close together. Here is a screen shot of that output:
Clearly, sites that do not pass, will not get a mobile-friendly label in the mobile results.
To try out the tool, go to google.com/webmasters/tools/mobile-friendly.