You should have seen how he looked in SMT IV....
http://img1.wikia.nocookie.net/__cb20130906211305/megamitensei/images/b/b9/Lucifer_smt_4.png

He does have a winged form though.
http://img3.wikia.nocookie.net/__cb20150226033803/megamitensei/images/b/ba/Lucifer_II_SMTIV.jpg

What you're seeing in SMTIVf is a redesign of these horrible designs.
Like this:

Redesign:
1. Design (something) again in a different way.
2. To revise in appearance, function, or conten.

Changing the fundamental concept is not the only thing that falls under that definition.
When there's a significant amount of changes, like redrawing something from scratch in a completely different artstyle, pose, color variety and detail, it's fair to call that a redesign as well.
I've used the term "cleaning up Nirasawa's work" as well before. You can type out a longer definition if you want, but if one word is enough to be understood by the reader, then I prefer that rather than typing out extra words needlessly. This is just semantics anyway. The point is, she looks completely different, and everyone is happy about it.

Huuuh? ... The design of Medusa is exactly the the same. Nothing has be added or removed;they just got a much better artist. Your definition is correct, but non of that happened here. If you took 2 artist and had them both draw  classic Cloud Strife, they will look different, not because its a redesign everybody just draws diffrent. 

 Your second sentence in your second paragraph is so broad. If I decide to to draw Sonic using water color, thats not a redesign. Changing Sonics pose does not pass as redesign. Changing color and detail  Is even a stretch - Ichigo wears tons of different outfits throughout bleach, I dont think anybody considers them a redesign. 

Classic Ifrit vs Nomura Ifrit is a redesign 

Classic Sonic vs Modern Sonic is a redesign 

Medusa left looks waaaay better, still same design though. 

Well it's hard to explain the difference in atmosphere, but I'll try.
One thing that can affect the atmosphere in a game is if the protagonist is silent, or vice versa. If they don't speak, and/or you can't see their facial expressions, like when you read a book, you often have to imagine certain things for yourself. While Flynn is a silent protagonist, his companions are not. And to be clear, voice overs does something for the atmosphere as well, so it's not like one is necessarily better than the other in that regard. But as mentioned before, SMT III's story is thinner than SMT IV's. Mainly because Demifiend doesn't travel with any companions. We also don't know his background or his aspirations before the world changed. There's also no real morality system in that game. You answer a few questions here and there, but they tend to be rather direct about that particular allignment, like "do you want to join us?". So you know very little about Demifiend, and that doesn't really change throughout the course of the game. And because of the way the game handles it's story, I felt that the less he said, the more fitting it felt for the atmosphere of the game. I'm not sure if that makes sense. (I don't think it would fit with all silent main characters in SMT IV though.)

Another thing that made SMT III's atmosphere stand out for me was the setting.
While in SMT IV, burning cars, poisonous puddles and ruined buildings with no electricity running were a common sight because of the struggle between humans and demons, in SMT III there seems to have been no struggle. Demon's simply took over, so you have the buildings nice and intact, but inhabited by demons instead. So their goals are not to get a daily fix of human brain juice. But just being part of that society in a peaceful way. Like Nyx running a bar for example.

And you can find Loki in there too, having a drink. And some others as well.
It's a very different feeling when you're part of a demon society, compared to civil war.
(Btw, being able to move around inside of buildings is nice rather than just looking at a picture. And on that note, I did find the graphical style for those things in SMT IV to be rather odd looking. It's almost something between 8-Bit and 16-bit graphics, while the rest of the game looked fine.)
So in SMT III you'll be running around in both Tokyo-esque buildings, as well as things that look like this:

In this particular area, I really like the red background. In SMT IV, when you're in Tokyo, besides the demon nests, you tend to feel like you're just in a ruined Tokyo. But the environments tend to vary a bit more in SMT III. In SMT III you get a strong sense that there's often a connection to another world. Every now and then you'll travel through something called The Labyrinth of Amala, and its 5 "Kapla". It's pretty much Hell.
There's more focus on symbolism and religious undertones in SMT III.
And I much prefer the quiet clean Tokyo mixed with a demonic world setting.

Then there's the music. I think both games have a great soundtrack though. But I got to give a bit of an edge to Nocturne.
Here's one of my favorites.

Just watch the first 45 seconds. Dante was the bees knees back in those days.
But the music tends to be more calm and suithing while exploring Tokyo. While I wasn't as fond of the music that often played in ruined Tokyo in SMT IV, like when you help the ring of Gaia.
And regarding presentation, scenes like the one in the video above weren't presented in such a nice fashion in SMT IV.

Both games are dark, but some times in different ways. You could often get an erie feel in SMT III. While some things in SMT IV gave me more of a... I don't want to use the term disgusted feeling, but it's the closest I can think of. Like the brain juice sucking experiments combined with the creepy 8-16 Bit style. Nirasawa's abominations sadly also gave me a bit of a bad aftertaste as well. While Kaneko's stuff is on point consistently in SMT III.

Regarding Akira, yes, compared to the rest of the supporting cast of SMT IV, he was more fleshed out. The reason I wanted more from him was because I found that part of the story very interesting. Tayama's part was also interesting, but I think we were told everything we needed to know there. With Akira, I wouldn't mind seeing a bit more. Because he was implied to have some sort of connection to Aquila/Akila. One Akira was very charismatic and felt like a natural leader. And the other was cowardly and weak, but had a strong will and sense of justice. How did they become so different? And perhaps he is one of the reincarnations of the main character. But in that case I wonder why Flynn's name is so different from the others. I would have liked to see more of that story. How Akira established his kingdom, and placed the demon guard between Mikado and Tokyo, etc.
So that the story came full circle. But it was a fairly brief visit to those worlds. So I guess that was one time I wished this wasn't a SMT game, and they could give us a bit more. As an example, an important supporting character in Persona 4 is Dojima. The main character's uncle and Nanako's father. You may know of him already. I guess his role as a supporting character is closest comparable to characters like Gabby, Yuriko or Akira in SMT IV. But compared to Akira, Dojima's script is probably at least 50 times longer. At least. But that's Persona, and this is mainline SMT. But I at least wanted to know a little bit more about him and those worlds, just because of how interesting it was. I remember walking around in Infernal Tokyo and came across an NPC, and behind him you could see the dome of the archangels. And he told me a story of how the archangels had left a long time ago, but that they also kidnapped little children some years ago and kept them inside. Wtf? What was that about? Maybe I missed something.
Then there's how the characters and Burroughs kept pointing out how Pluto, and the archangels underlings at the end of the game acted like machines. I don't know what the implication of this was or what it meant.

Anyway, in SMT III I wasn't as bothered by the Law vs Chaos system, because I didn't know the characters well to begin with, so their extreme allignments didn't come as a surprise to me.