Currently, copy/pasting is not supported between processes and objects. I believe this is because objects can contain things that processes cannot have, and vice versa.
Personally, I find that many objects and processes end up using the same elements (I have a lot of middle-tier objects). The situation I typically come across where I need to copy/paste pages between processes and objects is when I need to refactor parts of a process into a middle-tier object.
I've found a workaround to being able to cut/paste between processes and objects, namely that I paste the XML into a text editor, and then alter the first line of the XML, copy it again and afterwards I am able to cut/paste as desired.
So, if I'm going from a page in a process to a page in an object, I would alter this line in the XML:
<process name="__selection__Baxter"><process name="__selection__Baxter" type="object">You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.