It’s been made quite clear by Google that indexing of the web is primarily done by posing as a mobile device now, so that if our sites serve up different content to mobile visitors, it’s the mobile content that will appear in the search results. However, the ranking process is quite separate from the indexing one, and it appears that results can be quite different on mobile and desktop screens.
This is intentional. Google knows from serving up identical results on both types of device that what people click on differs, so it’s quite aware of what the users of different devices want. On a mobile device, I’m sure it’s more likely to be local search results, for example. Perhaps image-based results or videos get better response on desktop devices. I don’t know. Google does though, and it ranks results with a suitable bias.
With the importance that Google now puts on page responsiveness, I wonder if poorly-presented pages do even worse in mobile search results than they do on desktop results. Another reason to put in the effort to speed up your site.