What planet would have no advantage of any kind over earth for making parallax measurements?
You have to ask yourself what is an advantage when parallax
measurements are being made? . . parallax happens when you move to
a different place and the object you see look a little different,
the closest ones appear to have moved more than the ones that are
further away.
In astronomy parallax is created when the Earth is in opposite
points of its orbit. Stars that are close appear to have moved a
little, relative to the mass of stars that are a long distance
away.
Parallax was not observed before the 19th century, and the lack
of parallax was always used to 'prove' that the Earth could not
possibly be going round the Sun. It was only in the 19th century
that parallax was observed, but it was only very tiny movements of
the closest stars. It forced people to realise that the stars are
incredibly far away and the Earth does go round the Sun after all,
so it was extra evidence of the Sun being at the centre of the
solar system.
A parallax measurement is easier to make if the baseline is
longer, so the answer to your question is that Mercury and Venus
have no advantage for making parallax measurements.