Open both parts, split the window, control-drag from the cuurent sketch onto the surface of other part. It will not keep relations that are to other features of it's current part.
The only time Copy, Paste won't work. Is if you don't pick your face or plane prior to pasting.
I only use Copy, Paste - I have never used your method ctopher. Not saying it doesn't work. I have just been doing the Ctrl-C, Ctrl-V for a long time now. You just have to pick the face or plane first, then paste. It always works for me.