If you are a small business looking at options for a mobile version of your website, there are 3 main categories for doing so, but each comes with its pros and cons.
A responsive design finds out what the screen size of the device is, and uses the styling rules for that size to display the page. The HTML code doesn’t change, only the way it is displayed, so your customer will still have the same experience. The downside is that you can’t optimize for mobile devices only. The page may take longer to load, and can cost you in conversions.
A dedicated mobile site offers you a completely separate website that can be optimized with only the content you want to display. Pages are smaller, so they load faster, and you can design a unique mobile experience. However, since the mobile site is completely separate from the main site, the URL is different, and can cause duplicate content issues for some pages. Also if someone shares a page from their mobile device on social media, someone on a desktop may view the mobile version rather than the desktop version.
Lastly is a responsive server side design. This method dynamically creates the displaying HTML code depending on the device requesting it. It provides a hybrid for both optimized code for mobile, and full featured code for desktops. The drawback is that this puts a burden on your server if you have a lot of traffic. Also, the device detection is not 100% reliable, meaning some mobile users may still receive the desktop version.
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http://smallbiztrends.com/2013/03/design-a-mobile-website.html