First lets clarify the difference between a smart phone native app and a Web App.

A Web application is simply a website that is available over the internet and compatible with the device, smart phone or regular cell phone. A Native Application is an application designed for the device and built in the appropriate language to work in the devices operating system. The Native application may or may not use the internet, that all depends on the nature of the application and how the designer programmed it to work.

When to use or build a Native Application or just build a Web Application. It generally comes down to what the primary purpose of the application will be.