I imagine it should be possible to copy just the EQ settings. You can do a similar thing in Ultrabeat (copy and paste voices and sequences between voices and patterns).
In the meantime there is a little workaround to help:
1. Open space designer and select the EQ section you want to copy, to view it.
2. Press shift - Command - 4.
The mouse cursor turns into a cross hair.
3. click and hold and rubberband select (draw a box) around the EQ section.
4. Release the mouse button and a screenshot of that EQ section is taken.
5. Any screenshots are saved onto the desktop (picture 1, 2, 3...)
Open the picture and resize logic's window so you can see both the screenshot and Logic.
6. Open the space designer you want to copy the eq settings to and you can manually replicate the settings using your screenshot as a reference.