You don't actually need the Model Browser to perform this operation, just hold the Control key down when dragging one or more shapes and the shape(s) will be duplicated on the diagram. The advantage of dragging the existing shape from the diagram is that any shape settings will be replicated with the shape, as opposed to dragging the element from the Model Browser, which will give you shape defaults.
Shape settings include things like shape orientation, refmode expansion for fact type shapes, and relative positioning of child shapes (reading shapes, objectified object name shapes, value constraints, etc).
You can also drag shapes from one diagram to the other. This can be done using the 'Diagram Spy' tool window or with multiple document windows open on the same document. These features are discussed in 'General Use' and 'Window Management in Visual Studio' sections of the readme file, which is installed in the '%ProgramFiles%\ORM Solutions\ORM Architect for Visual Studio 200x' directory.
Note that you cannot directly control links between shapes (role player links, note connectors, subtypes). The heuristic used if a link is indicated is as follows:
If there is a relationship between element A and element B and a shape for element A is positioned on a diagram, then find the nearest shape for element B
If the nearest shape for element B is not closer to another shape for A, then create the link shape
The goal of the design was to eliminate lines across diagrams in most situations, and to never double-indicate a relationship (without step two, you could have one ObjectTypeShape connected to two FactTypeShapes for the same ObjectTypePlaysRole relationship). The one weakness in the system for multiple shapes that are very close is that the 'nearest shape' is based on the center of the shape, not the actual connection points. This means that the final connection line for the chosen shape pairing may in fact be longer than another available line to a different shape. For general use, however, the current algorithm 'just works' in the vast majority of cases.