I get the shopping experience is better on Amazon's app and because they may have put some smarts on the iPhone to offload servers and provide a snappier user experience. Or maybe you want to work disconnected. So there are technical arguments in some cases.
I suppose you could argue that being in iTunes gives you some kind of advertising angle, and maybe you can charge for the app (which the big dogs don't do) but a small specialized company might.
I'm currently considering ways to bring a mobile presence to my website and don't have a lot of experience in this space. I'd like to see what the Slashdot community has to say; iPhone app or mobile version of a website and why?