Combining large interactive surface computers (e.g., digital walls and tables) with smaller, multi-touch surface devices (e.g., smartphones and tablets) provides groups of users with both private and shared workspaces during collaborative (or competitive) activities. Such multi-surface environments introduce the need for effective interaction techniques that enable the transfer of digital content from one device to another, commonly known as cross-device transfer. Utilizing popular existing cross-transfer methods, such as Pick-and-Drop, in a multi-user multi-surface environment, however, require systems that can distinguish between users in order for the environment to accurately know who is transferring what content to what device. Yet, most commercially available digital tabletop systems are not capable of distinguishing between different users. Therefore, existing cross-device transfer methods must be adapted to work in such a user-information limited context. This paper presents a user study comparing the effectiveness of two adapted transfer methods in the context of a strategic digital tabletop card game task. The two transfer methods included a virtual portals-style method, called Bridges, and an adapted Pick-and-Drop method (A-PND). The studied transfer methods both supported the high-levels of card-transfer between private (tablet) and tabletop surfaces required by the game task. Also, participants' reported preferences were equally divided between the two techniques. An in-depth qualitative analysis of the study data revealed that each transfer method provided unique advantages and disadvantages for the game task, which aligned better or worse with different players' personal task goals.