I think it depends on the site/application. From what I have read general websites are better suited for the reactive/responsive approach whereas if the goal is to create a more native application experience then an app is the way to go.
As for the trend itself... I'm not sure. I think there will be a healthy number of both approaches in the future since there will always be a large number of websites but also as phones get better native apps will perform better and provide better experiences.
Using my workplace as a very small sample size, we have only been asked about an app two or three times, and once we tell the client that it will require much more development time (since you need to develop an app for iOS, Android, Blackberry, etc.) they immediately ask for the reactive/responsive solution.