Google now will use the mobile version of a web page for indexing and ranking since the shift towards Mobile first indexing, to better help mobile users find what they are looking for. Since 2015 majority of the searches happening on google.com have been on mobile.
Google will have one index search for results i.e not a mobile first index that separates it from the main index. Google will give priority to mobile web pages to index the web.
Mobile site have played an an important factor in how site are ranked but its not the only factor. The quality of content & best information will take precedence and appear higher.
Google has started the process of boosting the rank of mobile-friendly pages on mobile search results. Google gives a lot of priority to site speed for mobile search. Google has downgraded slow loading sites on mobile.
Google does not plan to shift all sites over to the new mobile-first indexing. It is just the initial phase.