Before a recent patch change, the Colossus used to go obsolete upon Navigation:
Goes obsolete once any player researches the Navigation technology.
Pretty clear wording.
The Great Wall, however, is a little more ambiguous:
Upon discovering Dynamite, The Great Wall becomes obsolete.
The question is, whose discovery of Dynamite? The owner of the wall? The enemy trying to walk inside the wall's owner's territory? Any player, like the Colossus?
Best Answer
The Great Wall will become obsolete when its owner researches Dynamite.
That seems to be the case in general as well: unless stated otherwise, the nation that built a wonder or troops has to be the one to research whatever technology obsoletes them before that happens.