Well it can be hard to tell which one is the "legendary hero" that is mentioned. The tunic Link wears holds some level of importance to many of the deities of Hyrule as well as the commoners at a later date. When it is mentioned by the people of Outset Island and the Deku Tree of Wind Waker we are led to believe that they can only mean the Hero of Time of OoT. There are numerous mentions of OoT Link and the seven sages throughout the game. In TP there are really no references to the events of OoT except what the player can pick out for themselves. However the Light Spirits do mention the tunic of the hero early in the game.
The light spirit Faron spoke of the legendary hero when giving Link of TP the green tunic.
Look at your awakened form...
The green tunic that is your garb once belonged to the ancient hero chosen by
the gods...
His power is yours. His is the true power that slept within you.
Your name is Link.
You are the hero chosen by the gods.
The Deku Tree also mentions the Garb Link wears as the garb of the Legendary Hero and not that of the Kokiri. This I think is interesting as a young Hylian wearing a green tunic should have reminded him at least somewhat of his own children. They all had the look of young Hylians in green tunics and hats. I think this might be significant.
That garb you wear...
Could you be the legendary hero?
Has the king at long last found the
Hero of Time?
What is the matter? Do you not understand
the ancient Hylian tongue?
So...you are not the Hero of Time.]
I must apologize. I was in error.
I saw your clothing, and suddenly I felt a
longing for an age gone by... That longing
caused the ancient tongue to pass my lips.
It might be possible that the tunics the Kokiri wear are based on the green tunic of a past Legendary Hero. The Deku Tree told Link in the game that he knew that he was a child of destiny
It seems the time has come for the boy without a fairy to begin his journey... The youth whose destiny it is to lead Hyrule to the path of justice and truth... Navi...go now! Find our young friend and guide him to me... I do not have much time left. Fly, Navi, fly! The fate of the forest, nay, the world, depends upon thee!"
Giving Link a green tunic at the time could have been a part of his preparing him for being the future hero.
Several time a helper or mentor figure has given Link the green tunic before he begins his journey. On outset island Link gained them from his grandmother to commemorate the legendary hero. The Link of ST gains a recruits uniform from Hyrulean soldeirs which is a green tunic possibly meant to remember the hero of WW, The Deku Tree might be doing the very same thing with Link of OoT. And in the demo of SS, we see Link putting on the familiar green tunic before setting off to the world below the clouds.
Another past theory that I have made on the tunic was that Green appears to be the color of Farore the goddess of courage. Everything that represents Farore, from the statues, symbols, pearls, spells, spiritual stones, and representations are always green. The holder of the triforce of courage represents Farore, normally wears green. And the servant of the goddess the Deku Tree that keeps the Kokiri Emerald and later the Goddess pearl is green. Leads a tribe of people that wear green, and normally is connected to the forest. Obviously the color green is sacred to the goddess who's triforce piece the legendary hero holds. So it does make sense that the hero who's main attribute is courage would wear green.
When Faron gave Link the green tunic of the hero of the past, he also said that "his power is yours." Which many people do consider the point in time which he obtained the triforce of courage. It might be possible that the Link of SS who helped establish Hyrule and form the Master Sword was well remembered by the deities of Hyrule, while the common folk most remember the previous hero that last saved the kingdom in each era. In the minds of both the current hero is wearing the familiar costume of the "Legendary hero" while that definition may be different. The Kokiri wearing green tunics of the hero of old could be just the Deku Tree remembering "an age gone by" even then.