Map is used to map a complete subresource - for buffers that means the whole buffer, and for textures that can mean a lot of different things depending on the dimension, array size, and mip levels. UpdateSubResource has the ability to update only a portion of a subresource, which can be an advantage in some cases.
I personally use Map to update my constant buffers in Hieroglyph3, but I think either method can be used...
So, you can update a portion of a vertex buffer with UpdateSubResource then? I'm just wondering how I would pass the offset within the buffer and the number of bytes to update to the UpdateSubResource method? Can you use UpdateSubResource to update a portion of a constant buffer?