As the name suggests, the Full Tech Tree option grants all players access to the full Technology Tree, meaning that all players can train every unit and research every technology in the game, but lose all their civilization bonuses.
In Age of Empires, every civilization becomes exactly the same in terms of gameplay. Non-standard units such as Fire Galleys (which are not recognized as a unit in the tech tree) are not available; every civilization gets access to Catapult Triremes instead.
In Age of Empires II, the Full Tech Tree equalizes all civilizations entirely with the exception of their unique units. Civilization and Team Bonuses are removed in return as well as unique technologies. Thus, the full technology tree grants the Native American civilizations access to cavalry and gunpowder, and all the other civilizations get the Eagle Warrior.