My vote goes to The Woodsman. I saw it recently and loved it, plus it closes at the end of the month. The puppetry is great, the set is beautiful, and the actors do an amazing job of getting the story across with little to no dialogue.
It depends what you're looking for. The Woodsman is a darker show (literally and figuratively) with a fairly sparse set and one violin with the ensemble providing some singing and vocal accompaniment. There's almost no dialogue and it tells a somewhat angsty story about voicelessness/subjugation, masculinity, and family. There's also a love story of sorts.
Tuck Everlasting is bright and colorful with a beautiful set, lighting, and costumes. There are a lot of straightforward musical theatre songs, a few that I enjoyed (though the boards tend to disagree). It seems targeted more at children but the cast includes Broadway veterans that adults might enjoy seeing. The story is about family, loss/death, and a typical young girl's coming of age story. There are love stories of sorts but they're mostly glossed over.
I haven't seen The Woodsman, so I can only weigh in on Neverland and Tuck.
Both are beautiful and tear-jerkers. My vote right now would be with Tuck, simply because Neverland has already announced the tour and I don't think the cast makes that big of a difference. Tuck on the other hand is gonna close soon, sadly, and even if it does end up touring, you really want to see this cast! So many Broadway vets, and Sarah Charles Lewis is just doing a phenomenal job. I can't believe this girl is literally (like her character) only 11!
The Woodsman for sure, if those are your only options. Finding Neverland is going on tour, Tuck will probably have a good regional life, but The Woodsman is closing and the amazing production elements will be hard to recreate in regional productions. Stunning show.
I haven't seen the Woodsman yet but am seeing it Thursday thanks to this board. :) Very excited.
Regarding the others, Finding Neverland is far from my favorite show but I enjoyed it quite a bit--more than I expected. I was entertained. I didn't care for Tuck. I just felt like it was more of a show for people taking kids. I was pretty bored.
I know others felt the opposite and I don't know that I can articulate why I liked FN and didn't like Tuck in a way that will be helpful...
I guess even though I haven't seen the Woodsman, from all I've heard that would be my recommendation. I sense it's very different from the other 2 though.