Device Compatibility
There are certain sites that are specifically designed for mobile devices and won’t structure on desktops or any other device. Mobile sites have a specific design that won’t work anywhere else, which is the key difference between them and responsive sites. Responsiv
e sites have a script built in that allow them to adjust to any kind of platform they are put on, allowing your site to look sharp on multiple devices. So, while a mobile design can be great if your just looking for something to look good on your phone, a responsive design is the best option if your site is going to all devices.
Need for Separate Sites
A mobile site will require you to have another site if you plan on having a site expand to desktop browsers and other future devices. This can end up costing you more money in the long-run as you will have to buy more domains to accommodate your expansion. A responsive site allows you to have one site for all future devices, saving you time and resources rather than attempting to build your site over again. However, if you plan on just having one site set for mobile and nothing else, a mobile specific site will still work for all next generation phones and tablets.
SEO Differences
If you do in fact plan on having multiple sites, using a mobile specific site may not be the best plan if SEO is a concern. A mobile site will constantly redirect your site to the desktop friendly one, which can hurt traffic from your main domain and hinder your rating. Responsive sites won’t have this problem as they will only go through that one domain, taking it easy on your SEO rank.