Each product is different, some need the level of access that a full native app can provide and for other services it makes no sense to do anything other than a web app. There is no single answer that caters for all but in some cases it might be feasible to do either and the choice comes more down to which it seems users are simply likely to prefer for one reason or another.
There are arguments in both directions - browsers today are fast and there are many mature technologies to build on. They also provide some degree of cross platform benefits (depending on how far back you need to support IE). The same can be said about native apps although in many cases the user experience particularly for getting up and running isn't nearly so smooth and simple (this is something we are trying hard to address with JWrapper).
Lincoln Murphy's interview with Office Drop over at sixteenventures provides some interesting insights though. Aside from the fascinating drag into a Freemium model as a result of negative reviews posted by mobile users with fundamentally different expectations around the apps marked 'Free', they also found that their heaviest users (who were apparently also their most 'willing to pay') were strongly pushing for an app over their existing web UI. It seems this wasn't to do with issues with their web UI as they had invested heavily in it but just that these users preferred an app as they felt apps worked better in their workflow.
This wasn't something they expected in fact their company ethos to this point had been that they would go with a pure web UI and entirely avoid native apps but the evidence ultimately pushed them in the opposite direction.
This push and eventual shift is reminiscent of the early days of the iPhone. When the original iPhone was released there was no 3rd party SDK and no capacity for developers to build native apps for the device, the reasoning being that developers could build web applications that "would behave like native apps on the iPhone". Ultimately though pressure from developers led to Apple releasing the SDK and the App Store is now about to break 10 billion downloads.
End users aren't really interested in the ideological or technical reasons behind an app implementation - they care about what the app can do, and works best for them.