Unfortunately both supersonics are rotting away quickly...
If you look at the sorry state of some 10-15 years older aircraft in that museum, I am afraid both airframes will be lost within 20 years.
Luckily at least 7 Concordes are preserved indoor (Scotland, Bristol, Yeovilton, Duxford, Toulouse, Washington, Paris), for the Tu-144 the situation is worse. The one in Monino still looks OK after 30 years in the open...