Let's take the Facebook application as an example. Why did they develop an application when the users could just access to their page and do the same? For me that represents more maintenance and more cost because for each feature added to the web application that feature will have to be added to the smartphone application as well.
So why would I want to develop more than once (for each patform iOS, Android, etc) when I could just have one web application? What benefits do I get? The only one that comes to my mind is GPS feature.
My question is more oriented towards business applications that are going to be used only by some members of the company, it's not about selling the application (private use). So contrary to what some answers say about that by developing as a smartphone application it will benefit from more sells because of the "smartphone stores" for me this point is not important because the application is for private use.
By developing the application as a web application it means that it can be accessed through smartphone browser and also in a PC (any capable browser), but developing as a native application would limit this to only some kind of smartphone so we would be limiting the use. On the other hand developing it as a web application means that in order to access the application an Internet connection must be available.
So keeping this in mind how would you convince your boss to write the application for a given smartphone platform (iOS/Android) vs developing it as a web application?