I work for the National Air and Space Museum. With aircraft, it is easy (and
tempting) to takea representative type and paint it to resemble a famous
aircraft.
 
However: a personnal experience regarding display of artifacts vs.
reproduction: As I showed an interested researcher around our off-site storage
area, he continually asked "You mean that's the REAL one?" He stared in awe at
the (real) Enola Gay and was amazed when I answered his question that the
Wright Flyer in the Mall museum was (you guessed) the REAL Wright Flyer.
 
When an artifact is directly connected to an historical event it does matter
to the public that the displayed item is the REAL artifact. People tend to
look interested in the reproduction Wright Flyer at Kitty Hawk, NC; they seem
more awed by the original hanging in the National Air and Space Museum in
Washington.  (And yes, the Kitty Hawk aircraft is correctly labelled as a repro
duction).
 
It's a matter of mystique, but yes, it does matter to the visitor.