Mobile friendly websites are increasingly important, not just because of ever increasing numbers of users being on mobile devices, but also because it has a bearing on your rankings with Google.
There are always arguements for and against "responsive" design and mobile specific. We recommend the latter for several reasons. Responsive is always a compromise on both ends, the main site suffers from a design perspective and often doesn't cope well (ironically) with different screen sizes. Likewise the mobile version.
Don't take our word for it, test your site on Google's test page