This is in terms of artwork. I chose not to go for a poll, because I´m also curious how people see the rest of them.
For me it´s;
Kabutops
Magikarp (I like it a bit better than the Gyarados, don´t know why)
Gyarados
Tyranitar
Noctowl
Mewtwo/Steelix
Charizard
These are the ones I all like. I don´t care much for the Raichu and Celebi at all.
If we’re counting Mew, that would probably be my #1! In general, I like them all quite a bit except Celebi, haha.
Mew
Celebi
Magikarp
Noctowl
Gyarados
Mewtwo
Tyranitar
Kabutops
Raichu
Steelix
Charizard
I only own my top 3 because they were the only ones I actually wanted, Noctowl through Tyranitar are alright. Not a fan of the rest
It’s hard to put them in an exact order. I would tier-list them as such:
S-Tier: Mew, Magikarp, Gyarados
A-Tier: Mewtwo, Tyranitar, Celebi
B-Tier: Raichu, Charizard
C-Tier: Noctowl, Kabutops, Steelix
My order would probably be this (I know you’ve said just Neo, but there aren’t too many cards with Shining in the name, so I’ve just included all - but feel free to focus on just the underlined ones from the Neo era 
):
Although I always liked the triple-star rarity of the Neo Destiny Shining Pokémon, I’ve never been the biggest fan of their artworks if I’m being completely honest.
As for Shining Gyarados, I consider it one of the best artworks of the TCG. 
Greetz,
Quuador
I’ve come to the conclusion that I don’t really care for any of them. Sure, Gyarados and Magikarp are decent by default and other than Steelix and Mewtwo I don’t hate any of them but it just feels like I’m going through the motions whenever we rank them. I do enjoy the colors on the Raichu, probably my favorite from Destiny, which probably would be Tyranitar if it wasn’t for the Fire energies. If I was still spending money I’d rather buy Base Blastoise or Ruby Sapphire Dustox 50 times over before buying any of them.
I included English Shinings from Neo Revelation and Neo Destiny.
Charizard
Kabutops
Mewtwo
Raichu
Tyranitar
Noctowl
Steelix
Celebi
Any list without Imakuni? is objectively wrong.
Japanese Shining Gyarados > Japanese Shining Magikarp >>> Japanese Neo 4 Shinings >>>>>>>>>>>>>> English Neo Shinings
Surprised Raichu is lower on most people’s rankings, I would almost give it the #1 spot
The good: Kabutops, Mewtwo, Gyarados, Raichu
The bad: Noctowl, Tyranitar, Magikarp
The ugly: Charizard, Steelix, Celebi
Lot’s of different opinions on this one. Love that.
For me the problem with the Raichu, Charizard (although I still lije that one) and Celebi is the angle.
S: Gyarados, Tyranitar, Mew
A: Magikarp, Mewtwo
B: Kabutops, Raichu, Steelix, Celebi
C: Noctowl, Charizard
Edit: oops, forgot Charizard…
