For me, one of the issues with the films is that this was the emotional peak of the series and it's in the first film!
The only thing that comes close to me is when Sam carries Frodo on his back, which is a good payoff for all the slightly funny scenes of them making moony eyes at each other while pledging eternal (love) friendship. I mean, I love those scenes but probably not for the reasons that Jackson intended.
And yeah, I'm one of those stone-hearted types who found the endless goodbyes at the end of the series overlong, repetitive and not particularly moving.
Yes, I admit to not being as a big a fan of the books as others so that obviously plays a role in my reaction.
I actually prefer The Hobbit (the book of course) for its compact plot, terrific villain, more successful humour and more engaging protagonist, all imo of course. Thank God that Jackson cut Tom Bombadil from LotR as he almost made me quit the book during his section, which couldn't end soon enough for me. Sometimes Tolkien turns The Twee up to 11 and I find it hard to take.
When it came to the LotR books I also feel like Fellowship is the strongest part of the book. Shelob is a later highlight in the books and the films but I experience almost everything after the battle with the Balrog and the death of Boromir as anti-climax.