2D are you out there?
I am
Sorry for the silence, I lost interest for a moment
I would support what Charlie says. If your licences are standalone and not dependent on one-another, you are free to exercise their privileges without limitation. In situations where both licences are valid, you are free to choose whichever licence fits the circumstances required most appropriately. Where only one is valid, the other licence becomes irrelevant.
So, if I have an FAA and a CAA plain-vanilla PPL, the circumstances will dictate which privileges I can rely on. Here are a few examples.
If I am in a G-reg aircraft in the UK, I can rely on either PPL and on the basis of my my FAA PPL and ANO Article 21 4a, I can fly out of sight of the surface, whilst remaining VFR.
If I am in an N-reg aircraft in the UK, the same is true.
If I take my N reg aircraft to France, my UK PPL is no longer valid for piloting that aircraft, and the only valid licence is my FAA PPL. I can still fly VFR on top because my FAA PPL says so, and because it is in compliance with the French definition of VFR.
If I take a G-reg aircraft to France, the only valid PPL is my CAA PPL because the French do not recognise an unendorsed FAA PPL for the purposes of piloting a G reg aircraft. (this is true in most of Europe). So I must rely on my CAA PPL privileges which do not allow flight out of sight of the surface, even though the French VFR definition does.
As you can see, this is all a bit painful. Generally speaking, if either the country you are flying in, or the aircraft's country of registration is the same as a licence you hold, then you may exercise the full privileges of that licence. It is not totally watertight, but it works most of the time