In this paper we present TangiWheel, a collection manipulation widget for tabletop displays. Our implementation is flexible, allowing either multi-touch or interaction, or even a hybrid scheme to better suit user choice and convenience. Different TangiWheel aspects and features are compared with other existing widgets for collection manipulation. The study reveals that TangiWheel is the first proposal to support a hybrid input modality with large resemblance levels between touch and tangible interaction styles. Several experiments were conducted to evaluate the techniques used in each input scheme for a better understanding of tangible surface interfaces in complex tasks performed by a single user (e.g., involving a typical master-slave exploration pattern). The results show that tangibles perform significantly better than fingers, despite dealing with a greater number of interactions, in situations that require a large number of acquisitions and basic manipulation tasks such as establishing location and orientation. However, when users have to perform multiple exploration and selection operations that do not require previous basic manipulation tasks, for instance when collections are fixed in the interface layout, touch input is significantly better in terms of required time and number of actions. Finally, when a more elastic collection layout or more complex additional insertion or displacement operations are needed, the hybrid and tangible approaches clearly outperform finger-based interactions.