It was really not too long ago that Google started to include the mobile responsiveness of websites as an element to determining the SEO of a website in mobile search. This makes sense, of course, since Google are all about providing the best user experience for a web user online – if this means promoting websites that are better viewed on mobiles since they have a mobile theme, then so be it.
However, it still appears that the vast majority of traffic still comes from computers, both desktops and laptops. Saying this, there is an emerging market which is gaining more and more traffic every year, being the mobile sector. People find it much more convieniant to use their mobile for searching than a laptop or desktop.
So, straight away, we already have one answer to the title of this article. You should be concentrating on SEO for mobile more since the traffic that is coming from mobile devices is increasing year on year, whilst desktop traffic decreases.
 
If you still need some more reason to concentrate on mobile users for SEO, take a look at the search engine console analytics for one of my websites.
The graph accounts for the previous 28 days and illustrates that, for desktop searches:

• The average CTR is 8.3%
• The average page position is 16.6

These stats are quite meaningless, especially with the fact that you do not know what website I am referring to and what sector the website is in. However, take note of these numbers since this is for desktop traffic.
If we filtered to look at mobile traffic, here is what we find.
It is clear straight away that mobile appears to have better SEO for this website of mine, with a CTR that is 0.72% higher and an average page position that is a whole 10 results lower.
 

Analysis

With this, it needs to be taken with a pinch of salt, like any analytics that does not have much data (for example, I am only looking at one website and not several).
But, what we can conclude is that mobile appears to promote better traffic. This is because the CTR is higher and the average page position is a lot less too, increasing the exposure of articles on mobile.
If mobile is to increase year on year with traffic, then it is promising to see such beneficial stats next to mobile web users.
Saying this, the average page positions cannot be directly compared that easily, since the number of results on mobile is fewer than on the first page of a desktop browser.
The CTR of the organic links can be compared, where mobile traffic generates more traffic from a higher CTR. For this reason, you would be mad to not invest time to improving the SEO of your website for mobile traffic, especially when the future very much appears to be mobile for the internet.