The evidence is mounting to the point that retailers ignore the research to their determinant. Consumers use mobile websites to complete purchases but prefer mobile apps to share information. This preference is crucial because it affects measurement related to the project's success or failure. Mark Walsh provides the money option:
(Enrich) is a strategy focused on driving transactions and measured in overall purchases, purchase size or frequency, and same-store metrics.
(Engage) is geared toward building brand affinity. The focus is on bringing shoppers closer to the brand to drive interaction.
A study by Yahoo and Ipsos (shown in the below table) confirms much of Walsh's money option. Consumers prefer to use a mobile web for purchase-related activities and a mobile app for information-sharing related activities.
This question exists because of money. It costs money to optimize a website with some estimates of creating and maintain a website that is optimized for a mobile device at $100,000. An app costs far less to develop but costs more to maintain. Furthermore, the retailer has to create and maintain separate apps for each platform including Apple's iOS, Android, Blackberry, Windows and Palm. Without an app for each platform, the retailer risks losing customers. If a retailer allocates financial resource toward developing a mobile app and measures success by sales revenue generated, then the project's outcome will only disappoint the retailer.
However, each tablet sold renders this question moot because tablets can properly render a website designed for a laptop or desktop computer. No need and no cost incurred for an app or an optimized website.