I would say that it depends.
What are you trying to achieve? Are you trying to make something that people will use in a particular way (and probably regularly) from their mobile device, with particular functions, like an app, or that people will browse like a website?
Website-style tend to be "I'm using this website, it happens to now have a version of it optimised for mobile usage". You're producing the same content, it's just optimised for mobile usage.
Things that may be better done in app style tend to be things that are used regularly and where the workflow tends to be different on a mobile device to what it would be on the normal version of the website, or providing a different set of functionality.
What Matt says about the importance of user perception is true, but I don't agree entirely with what he says about never being able to get it exactly right; with care (and leaving a good deal of it to web-based mobile app frameworks like jQuery Mobile or Sencha Touch), you can make it act like a native app in a convincing way.
My advice is to review your goals and decide from them which is more appropriate based upon what you are trying to achieve.