Unity3D has native multimonitor support in recent versions. The API documentation suggests that this is tied to connecting each display to a camera view. Is it possible to,
In addition to the other answers, if you really want to display a different scene on another monitor, you could make sure everything in that scenes is on a specific layer. Then on the camera in that scene set the cullingmask to render only that layer, and on your main camera exclude that layer. Then just load the scene additively as was mentioned.
This is basically how Unity's previewer works too (although rather than a scene it instantiates a hidden prefab).