Naboris is the best beast from a gameplay perspective. It has the best map mechanic and the puzzles that are based around it are top notch. The electrical theme on the inside makes it aesthetically pleasing and getting inside was actually difficult rather than an annoyance like Medoh. It also has the most fun boss fight as far as the blights go, but I never actually found Thunderblight as difficult as a lot of people seem to.
Ruta was my first divine beast and I thought it was really cool how the map mechanic worked and how the puzzles were structured around it. It was a layer of puzzle solving I wasn't used to so I thought it was really neat. The inside is pretty nice with the water faucets making for a nice background aesthetic (I've always liked water themes in general) and it has, as far as the blights go, the most difficult boss fight for me. If there is one thing I would criticize this dungeon for, it's that there are 7 or 8 different spots you can move the trunk to but I believe you can solve the entire dungeon only using 2 or 3 trunk positions once you know how to, which I feel like they could have done more with it. Overall a solid dungeon though.
Rudania and Medoh are both a little interchangeable to me, but I think I have to give the edge to Rudania. Starting in the darkness was a really cool idea and if they had kept that idea for the entire dungeon it could have been top-tier. But, sadly once the lights come on the whole dungeon becomes a bit of a let down. With the beast only tilting one-way, it is extremely easy to figure out the puzzles and overall this dungeon presents very little challenge. The boss is also boring, being essentially just King Dodongo put through the Blight Ganon cookie-cutter. The atmosphere outside also doesn't look good at all. This one is third only because of the first portion of the dungeon. Had it not been for the darkness, this dungeon would probably be number 4. It's a shame because the stealth portion before it is my favourite "beast battle" in the game.
Medoh is down here because, like Rudania, it's just kind of bland. The puzzles are meh, since the beast only tilts 45 degrees it's very easy to predict what you are supposed to do. I do appreciate, however, that the entire beast can be solved without once opening the map screen if you are clever and creative, which does give it some more points. Being high up in the sky is also quite cool and this would probably be my favourite beast if it was in terms of atmosphere alone. But there is too much that brings it down; easy puzzles, a bland boss fight, mediocre mechanics, etc. It also has a really annoying entrance fight (at least for me, I'm not very good at using arrows in this game lol). So overall, gameplay wise, this is my worst divine beast.
So now I guess I'll rank them based on their design? I assume this is just exterior design.
Medoh
Ruta
Naboris
Rudania
They all look really good, I will say that much. Rudania is the weakest in my opinion, but I still love the way it looks. I also love how you can see it circling Death Mountain as early as the very first cutscene in the game.
So what order did I do them in initially? Well, I've already said what my first was, but I'll repeat it.
1. Ruta
2. Medoh
3. Rudania
4. Naboris
If I was to add the Final Trial in here, it would be number one easily. Incorporating puzzles that match the theme of the previous divine beasts was a great idea and some of the puzzles are genuinely challenging. The atmosphere is great and the way they used a remix of the Shrine music really makes it feel like a final trial. The boss fight is fantastic, being the best fight in the game in my opinion, and the whole dungeon just feels climactic.