If you want vertex colors use Filters -> Sampling -> Vertex Attribute Transfer, click the appropriate boxes to transfer color, and select the appropriate source and target meshes.
If you want a texture, you first need UV coordinates - the easiest and messiest way for an arbitrary mesh is to do Filters -> Texture -> Parameterization: Trivial per triangle, then use Filters -> Texture -> Transfer: Vertex Attributes to Texture. This can cause seams to appear. For my messy meshes I use the Smart UV in Blender and export it out as a .obj, then import it into meshlab and use the aforementioned Transfer: Vertex Attributes to Texture filter.