As you probably know 'Responsive Design' refers to an easy way to dynamically customize interfaces for different devices and to serve them all, with no need for a separate mobile domain.
With a responsive design for mobile and tablet you can see the interface transform dynamically by viewing it in a desktop browser and resizing the window. There are other differences such as the menu. On many desktop websites, users have drop-down menus to access nested categories in a single move. But in mobile interfaces, each set of navigation options is usually presented one at a time; for example, with iPhone-style sliding drill-down menu panels.
Responsive design solves one major problem, and very elegantly: how to adapt visual interfaces for mobile, tablet and desktop browsers. But when unifying a website, you have to solve problems other than how it will appear in different browsers, which could make the task much more difficult than you first realize. A solid design has to account for differences in interaction when using mouse pointers and when using touch gestures, as well as the bandwidth constraints on mobile users.
From the below trend which is structred between Responsive design and Mobile design, here is how stats are since 2011 till Jan of 2013. Clear Responsive Design is cruising way ahead of mobile design.
You might also have to restructure content according to how much information it makes sense to present on each screen. Mobile users are usually in a different frame of mind than desktop users. Compared to desktop usage they quite often will be standing up and walking around or driving, and sometimes just scanning their handset or tablet. This might call for less detailed content than what you would use for more focused desktop users.
Mobile users and mobile usage are growing. With more users doing more on mobile, the spotlight is on how to improve the individual elements that together create the mobile user experience.
You may be able to implement a responsive website that is suitable for all devices; but if that's not possible you may be better off with a separate 'Mobile Website'.