I love both these films.
"Remember the Titans" is a great movie. I particularly like the scenes when they're at training camp the most. That's the best part of the movie if you ask me, and the reason why it's as good as it is. The football scenes are nothing special and the characters on the team (not including any of the coaches and the little girl, when saying that), with the exception of Kip Pardue's character and the dude who played Petey, aren't all that good either to be honest. But it's their time at training camp that makes me love this film.
"Little Miss Sunshine", however, is tremendous from start to finish. It's another flawless film in this tournament. The writing, acting, look, drama, comedy... it's all perfect. Also, it's a film where you can't predict what's going to happen next. It's just a fun ride. While you enjoy sitting through "Remember the Titans", you can easily predict what's going to happen, but there's absolutely no way you could've done that with "Little Miss Sunshine".
In the end, "Little Miss Sunshine" is just far superior to "Remember the Titans" in every aspect, and deserves to go far in this tournament. "Little Miss Sunshine" easily receives my vote.