I'm also with the LOTR crowd, but a different section.
I like the whole series of scenes in Fellowship, from leaving Balin's tomb, the arrival of the Balrog, the collapsing staircase, and Gandolf vs the Balrog on the Bridge. I just think they are visually stunning, and in my opinion the following films struggle to match it visually, even if the story is better.
Would probably have to pick the descent on the collapsing staircase in Moria as the best overall. ("No-one tosses a dwarf ! ")