Google has tested countless designs and layouts for the sitelinks you see in both the desktop and mobile search results. But I honestly have not seen a test in a while around sitelinks in a while, that is until now.
Here is a screen shot from Ric Rodriguez on Twitter showing sitelinks with descriptions under them. So the first main snippet has less of a description line but the sitelinks sections all have short one line description lines.
Compare that to the normal sitelinks mobile interface with no description lines, although some expand:
Ric also shared a version with the sitelinks search box:
Forum discussion at Twitter.