That depends on your website and your business, it’s impossible to say which one of these methods are best for business.
If you want to compare between them you will find:
RWD have advantages in keeping same content, easily achieved with using (css, media queries, and HTML5), and cheaper to use with less time to adapt. However it’s not giving the user a fully optimized experience, not adaptable to user’s behaviors with mobile especially users not act the same, and websites with large file will need longer time to load with 3G connection.
AWD have advantages in speed since The HTML and CSS can be minimal and stripped down, UI and user experience related to user behaviors since you adapt the layout depending on it, and easily to transpose code to create native app that you can submit in apps store saving your team time from learning Objective-C or Java for Andriod. However you will need to create content for each and every device, which also expensive and but yourself on risk or branding consistency and confusing your audience.
So if your website is a corporate website or just a content that will display same information and same structure regardless the device, you can go with RWD. As for website with more events and user actions, go with AWD.
Sometimes, the best solution is a combination of AWD within RWD in order to obtain the same user experience objectives far more cost effectively and efficiently than by using AWD or RWD alone.
