So, I checked and the GPU rendering is taking almost no time - in fact even without rendering anything in Paint() but with continuous repainting enabled I get the same issue. Also, if I have another adjacent component that uses software rendering then the combo box behaviour is fine on this but not on the opengl rendered one.
I think the problem is related to how the two components are interacting with regard to being painted since I also tried an experiment where I obscured the opengl component with a window that always stays on top i.e. task manager. If task manager is positioned, obscuring the opengl component, so that the combo box only intersects task manager then the interaction stops being sluggish. If you slightly lower task manager so that a few pixels of the opengl window intersect with the combobox then the behaviour becomes sluggish again.
Its probably worth me mentioning another observation that led me to seeing this issue since they may be related. I found that if you have your juce program minimised on the toolbar and click on it to maximise it back up then any opengl rendered components don't get resized() or paint() called at all but the software rendered ones do. Hence the opengl regions are not refreshed. This is why I turned on continuous repainting and hence saw the original issue. The only time with an opengl rendered component where the response of an overlapping component is OK is when the opengl window has continuous repainting turned off and the opengl context is not being refreshed with new data, hence I presume it is not being repainted.
So, sorry for the very verbose mail but I hope this gives some clues to the nature of the problem and how it might be fixed or worked around.