I did not see 3 of the films listed above that were directed by Fincher (Zodiac, The Curious Case of Benjamin Button, and his remake of The Girl with the Dragon Tattoo), but here are my opinions of the rest of Fincher's films:
(1) Alien 3: a piece of crap film.
(2) Seven: interesting and suspenseful at times, but somewhat overrated IMO.
(3) The Game: highly overrated -- the suspenseful lead-up and good performances completely ruined by a ludicrous ending.
(4) Fight Club: a superb film, probably among the 2 best films Fincher has ever made.
(5) The Social Network: a superb film, probably among the 2 best films Fincher has ever made.
Now here are my opinions of Nolan's films (almost all of which I've seen):
(1) Memento: an absolutely brilliant film, among my list of all time favourite movies.
(2) Insomnia: a solid re-make of the earlier Norwegian film.
(3) The Dark Knight Trilogy (Batman Begins, The Dark Knight, The Dark Knight Rises): an absolutely brilliant take on the Batman comics, also among my list of all time favourite movies.
(4) The Prestige: an interesting failure -- at times gripping and fascinating, but deeply flawed IMO.
(5) Inception: another superb film.
So overall, based on the record above, I would have to say the Nolan is overall the better director, and so voted accordingly.