The simple answer is a bit obvious.

A native app is one that is installed directly onto the smart phone and can work, in most cases, with no internet connectivity depending on the nature of the app.  A web app works via web browser on the smartphone but requires either a cell signal or wi-fi to function.

The benefits of the native app is that it can work independently of the web, but most are pulling information or function from the web.  There is an aspect of “behind the scenes” in the native app that is presenting web content within the app itself sans browser.  The native app can work much faster by harnessing the power of the processor. and can access specific hardware like GPS.  In some smart phones the app can control devices and act as a controller itself.

The web app has the fortune of being used on various devices with the only requirement being a web browser and an internet connection.  As long as the web app is written for cross-browser compatibility then you’re a go.  The dilemma is that in contrast to the native app, it requires internet access and its operation speeds are dependent on the quality of cell signal or the speed of the wi-fi broadband you are connected to.  This also alludes to the fact that you have to be in range of either connection.  You might not be able to use the web app inside of buildings or in lower level facilities.  One other issue is you won’t have access to internal hardware such as GPS and other connectivity.

So it comes down to whether you want to sacrifice function for ease of porting to various devices.