depth of field - How does using a lens with some focal length on a full frame camera differ from using a lens with "equivalent" focal lens on a crop camera?

As an example, a 35mm lens on a crop body (such as Nikon DX) is said to be "equivalent" to a 50mm lens on a full frame body. Equivalent here means that they will have the same field of view, but what other aspects will change or stay the same between the two? I'm thinking about things like perspective, bokeh, and depth of field (assuming the same aperture being used on both lenses).