We are fans of responsive design for a lot of reasons, not least because it’s the approach to mobile that Google advises. When you look at the reasons it’s not hard to see why. In essence you only have one site with the value of any link to any of your pages shared across a single site rather than split across mobile and desktop versions.
Google actually recommend using responsive design as the optimal design methodology where possible. This means that the same url is serving all of the pages whether the user is on a desktop or mobile. It is just the CSS that changes how the content is displayed.
The benefits are:
If a user sends a link from a mobile site to a desktop user, the experience would be very poor as the user would view the mobile page on a desktop.
Google only needs to index once as all URLs are the same for mobile and desktop. Google just indexes once rather than indexing the mobile site specifically using its mobile Google crawler as well as the desktop site. And if it's better for Google it's better for your search engine optimisation.
You are not weakening your “link juice”. Instead any link to a page adds value to the whole site. If you had a sub-domain for mobile, the links to those pages would not add value to the desktop site as they would only reference the mobile site and vice versa.
It is more cost effective to develop a responsive design because the design automatically sizes to meet the resolution of the device it is viewed on. You don’t need different versions for different mobile platforms and different resolutions. This makes it more able to cope with changing demands of new phones and reduces development costs.
Responsive sites allow the content to be indexed which means Google can lead new visitors to your responsive site whereas you have to promote an app.
Any user generated content in apps cannot be indexed and searched by Google so it cannot add value back to your main site