Instrumentality...
Complementation...
Two similar projects...
Two different outcomes...

SEELE, the overseers of NERV, desired to evolve man into a higher form of existence using a project known as the Instrumentality of Man. In doing so, they had to artificially induce Third Impact, which would again see the death of half the world.

"..all must die too become one" - SEELE

Gendou Ikari, Supreme Commander of NERV, desired all men to form into one complete entity, where mankind would be able to fill and complement each other. The name of this project was the Complementation of Man. No one would die, but in turn, we would all loose our individuality.

"Death does not create anything" - Gendou Ikari

With two opposing intentions, conflict between the two organizations was inevitable. NERV had an upper hand in that it had Unit 01, and Lilith, but SEELE had a good deal of power behind it, as is seen by the special forces used to invade NERV in End of Evangelion. NERV possesed what SEELE needed to complete their dogmata, following the Dead Sea Scrolls, and they were willing to take what they needed.

Instrumentality is the first project to commence, when the X2 type Evangelions unite with Unit 01, to depict the Sephirothic System. It is at this moment that Third Impact occurrs. Unit 01 and the Spear of Loginus combine to form the Tree of Life.

Also at this moment, Ikari is attempting to control the future of mankind by controlling Rei. In doing so, he would be the overseer of man's fate, and would be able to dictate it to his desire. In more simple terms, he would become a god. However, Rei refuses to allow Ikari to control her, and in turn, hands mankind's fate over to of Shinji. This is where the two projects collide. The Tree of Life along with all the souls on Earth enter Rei, thus becoming one complete entity. Shinji however, chooses to return life to the way it was, or the way it is now. Hence all our souls return to Earth, save Yui Ikari, who stays on in Unit 01, to ensure mankind's existence for eternity.

"As long as there is the Sun, the Moon, and the Earth...
....It will be alright" - Rei Ayanami