A native application is an application that requires installation, with its own software. Such applications have some advantages, such as push-notifications and high performance, but installing the application can be an obstacle for the user. As for the cost, creating a native application is not comparable in cost with the development of an adaptive version of the site, such an application is difficult and expensive to promote in the App Store and Google Market.
The native application doesn't have any advantages for search engine optimization. In addition, the native app requires constant and separate support, and the development cost will be significantly higher than the cost of the adaptive version of the site.
A separate mobile version of the site is aimed for users of smartphones and tablets. The mobile version is a truncated version, that is, the site only works with the set of elements and functionality that is necessary for users of mobile gadgets. This version is much simplified in comparison with the usual desktop version.
The mobile version doesn't provide unnecessary functionality for the mobile user. In addition, in the mobile version it's possible to go to the full version of the site. By labor, the development of the mobile version of the site can almost be compared with the adaptive version, but a separate mobile version requires more expenses with subsequent development and support.
There're also disadvantages in the search engine optimization of the site's mobile version. The indexing includes pages with duplicate content, but with different URLs. In addition, an unpleasant factor is that you need to remember one more address of the site.
Similar to the mobile version, the way the site is displayed. Dynamic display for different gadgets uses different versions of HTML code, but one URL. There's a possibility that the search engine robot can get an incomplete version of the site and rank it worse than the adapted sites.