The question of whether to have a native app or a web app may not have come up yet, but it seems to be one that a lot of businesses are currently thinking about.
LinkedIn recently launched their new iPad app, and 95% of it has been built in HTML5: http://venturebeat.com/2012/05/02/linkedin-ipad-app-engineering/
The Financial Times decided to ditch their native app for a web app and have had some promising results: http://www.readwriteweb.com/archives/financial_times_proves_html5_can_beat_native_mobil.php.
There are many articles on this: http://mashable.com/2011/05/23/mobile-commerce-apps/ and http://www.useit.com/alertbox/mobile-sites-apps.html and: http://www.forbes.com/sites/fredcavazza/2011/09/27/mobile-web-app-vs-native-app-its-complicated/ and although twice as many people access mobile sites compared to native apps: http://www.internetretailer.com/trends/e-retailers/ the conversion rate between them are interesting (Apple has a higher conversion rate for native apps, Android is about the same, and Blackberry is lower).
Although from the technical point of view, an app can be largely be made to just run in a browser, the question comes down to support, and usage.
It would be really interesting to get your take on the situation. You can leave a comment below or reply to me on Twitter @paulrandall.