Firstly lets look at the type of mobile sites currently available.
- Responsive Design. Often referred to as “RWD” for Responsive Web Design, this design approach uses fluid, proportion-based grids, flexible images and varying CSS style rules to deliver different user experiences to desktop, tablet and mobile devices while maintaining the same HTML and URL structure. The site shrinks or grows according to device.
- Adaptive Design. Referred to by Google as dynamic serving, adaptive design serves different devices using the same URL structure, but it does so by detecting the device and generating a different version of the site’s HTML appropriate for that device. The site has multiple versions that are served through common URLs.
- Separate Mobile Site. Sometimes referred to as mDot (“m.”), this configuration delivers different HTML on separate URLs depending on the device detected. The usual arrangement is to have the desktop site located on the www subdomain and the mobile-friendly site’s pages located on the “m.” subdomain.
Now it seems to be pretty clear that Google prefers the "responsive" choice, not least because this type saves Google resources, Google might forgive bad code but you costing it money.
Now, does this translate into an improvement in ranking, well the jury is still out but the gathering momentum says yes, slightly, and likely to be more important in the future, so to put it simply when your site needs upgrading (if its not mobile friendly that's NOW) make sure it meets Google's requirements, there are a lot of factors, content, design, links, code, speed, structure and a lot more.