Both are good, but my preference is Lion King which, IMO, is excellent. Seeing the puppeteers in Nemo ruins the experience for me; I find them distracting. It's hard for me to stay in the "magical moment" when the puppeteers are moving about.
I vote for both of them. They are 2 completely different productions. Nemo is a Broadway style theater production of Finding Nemo. Lion King is a song, dance and acrobatics show to the music of the movie. Nemo is a traditional theater with the stage in front, Lion King has the stage in the middle with 4 sets of bleachers around it. They are both really cool.
We prefer Lion King. While Nemo is visually very cool, it went on about 15 min too long for our young boys. However, if your kiddos enjoy broadway they will appreciate both! I would suggest checking them out on YouTube if your still undecided.
I would personally choose Festival of the Lion King. It is considered by many to be a Broadway-level show. All the actors and dancers are excellent, and are dedicated to their craft. My favorite, though, is when this man plays Kiume. Here is some of the other things he has been in (he is the tall bald man):
I seem to be in the minority as well, but I very much prefer Nemo over The Lion King. TLK has some nice elements - I like the tumble monkeys, and I really like the bird lady flying high on a rope. But overall Nemo just works better for me.
Lion King is more popular. Both are quality productions.
I feel that LK is more predictable in terms of what you get. It's a live-action LK highlights reel.
Nemo is more interesting to me in that it delivers something different. Because it's a musical take on a non-musical it's more of a new experience.
Walking out of Nemo one might think, that was a unique take on something I'm familiar with, whereas with LK one might think, yep, that was the Lion King. Which to choose is a matter of personal preference.