Another vote for Lion King, and like everyone else, it JUST edges out Nemo.
Also totally agree with the unnecessary recap of all the songs at the end of the Lion King show. They were great, but it just adds a bit more time to sit in bleachers than you need....especially if you're with a toddler.
I am in the minority in that I like Nemo better. I like that it tells the story. I love the original song. It is unique in that the actors sing, talk, and operate the puppets at the same time (heck, I have trouble talking and chewing gum at the same time). Lion King is great too, though I think Nemo is more unique.
They both provide a lot of entertaiment and should both be seen. But because of the unique style of puppetry, music and songs, the coordinated scenes... Nemo gets my vote as must see. LK is good and has lots of fun moments but not as unique in how its performed.
I love them both, and they're staged so differently (Nemo is on a big, traditional stage, while the Lion King is theater-in-the-round, with sets on floats that are paraded in from the corners) and tell such different stories, with such different styles, that it's a bit of an apples-to-oranges comparison to try and pick a favorite.
That being said, I personally prefer FOTLK, simply because I find its music and theme to be more engaging to me personally. If you have time, though, I'd try to squeeze in both. For me, those two shows are easily the best live shows anywhere on Disney property.
I'd definitely say the Festival of the Lion King... but I haven't actually seen all of Nemo in years. Sitting in air conditioning, I have fallen asleep the last 3 times we've been to the show. Perhaps there is an amazing part in the middle that would rank in higher for me.
(This is the only attraction in all of WDW that I've slept through, yet it's been consistent!)