I see you're one of those that have difficulty understanding abstracts... Or maybe even interpreting obvious and plain text.
Archaic, you say the TV series ending shows the rejection of Instrumentality. That is false. To think that the TV series ending shows Shinji rejecting Instrumentality is idiotic at the least.
While the following contains the opinion of the FAQ author, I think it is true:
Q) Are the TV ending and Film ending the same conclusion to the saga?
A) In my view - No.
In the TV ending Shinji chose to stay with Complementation - it isn't even clear that Shinji had a choice at all. He is treated as little more than an example of the process of Complementation - which consisted if breaking down Shinji's link to reality. In the end, Shinji looks at the world of Complementation and smiling happily says "I understand! I can exist here!" He is then congratulated for his decision, by friends living and dead (Kaji), a healthy Touji with his leg still on, and even PenPen. A surreal ending scene to say the least. This ending is similar in context and theme to the ending of George Orwell's book, 1984.
Conversely, the film ends in the opposite manner. Shinji does have a choice and in the last moments of the film utterly rejects Complementation precisely because it eliminates the link to reality, it establishes a false paradise. Complementation is basically a cop-out, and Shinji has matured enough to realize this. The tone at the end of the film isn't a surreal, almost drug-induced, joyful "Congratulations!" for Shinji, but the cold and harsh reality of life.
Further, the Newtype Filmbook description for the scene states (literally):
"Amidst the many words of congratulations, a faint smile starts at the corners of Shinji's mouth (and spreads across his face).
A happy face -- that is the figure of the Complemented Shinji. This conclusion is also one form, one possibility among many."
(Translated by Bochan Bird)
Note, "the figure of the Complemented Shinji". Pretty cut and dry.
Remember that the TV series ending is shown from an individual internal perspective, while EoE is shown from a generally external perspective.
The TV series ending tells Shinji "Life has too much pain. Join everyone together to end that pain, so Man can live as one, without pain." They tell Shinji that he doesn't have to continue to exist in Reality, and that he can create his own if he accepts Instrumentality. But this is actually a lie to get Shinji to accept Instumentality.*
Shinji accepts this, and is treated to everyone he's known, even if they are dead (Kaji, Ritsuko, Misato, Yui, etc...). And they all congradulate him on his choice. It is a false reality. And it just ends there, as Instrumentality becomes complete and all of Man is reborn as the Single Perfect Being.
In EoE, Shinji is told the same thing, but rejects it. While pain doesn't feel good, it's what makes us human and separate entities. If Man is allowed to exist separate, then that pain is bearable. Thus, Shinji rejects Instrumentality, destroying Lilith, and returning the souls to the Earth, into the sea of LCL. Shinji and Asuka are also returned to Earth, and he strangles her to make sure they and their surroundings are both in reality, and to see if pain still exists. Asuka's reaction, Shinji's breaking down, and then Asuka's disgust shows that the result of the test was positive. Pain still exists, and Man remains separate beings.
*We see part of this in EoE as well. Shinji is terrified of Lilith as Rei, and doesn't accept. When Lilith switches to Kaworu, the only person in his life to tell him he was loved, he accept almost immediately. As Shinji accepts, Lilith switcheds back to Rei, and proceeds with Instrumentality.
