Oh shit, here we go again.
MUSIC
For me, music is probably the single most important thing in all media I enjoy. I like the music in most Rayman games, however Origins is the single exception. I even like Rayman Mini's soundtrack more. The reason is the lack of melody in a lot of tracks, and emotions that convey anything other than "crazy happy place". It's great to have a track or two like this, but there is just not enough variation.
Of course, I do enjoy a couple tracks, such as Lums of the Water/Glou Glou and its variations, "The Lums' Dream" and "The Abyss". Sea of Serendipity is the single world in the game where the tone changes from goofy to creepy and dangerous. At least, underwater, because the Red Wizard village's soundtrack still sounds like some crazy party is going on, like in every world before that. Again, it's not that I cannot appreciate tracks like that on their own, but you need variation, and this game doesn't have any.
Meanwhile, the Rayman Legends soundtrack is full of variation. It has calming tracks like The Enchanted Forest, ones with hints of sadness like When the Wind Blows (a much improved version of an Origins track) and to a greater extent, Lost in the Clouds (not used in the game, for shame), heroic tracks such as The Adventure Begins, The Tower of Babel (Medieval Theme in the OST), mysterious ones such as the 20,000 Lums Under The Sea themes (Dive Another Day and Mansion of the Deep are my favorites!). Yes, you still have the funny tracks such as Luchador, Infernal Pursuit, but the range of emotions is so much broader than before!
In short, it's not even a contest here. Rayman Legends simply has a much better soundtrack. Origins does not compare. A 2/10 rating is too high for that soundtrack.
Winner: Rayman Legends
For me, this already decides which is the better game as well, however I can discuss a few other aspects, I guess.
WORLD DESIGN
The first world in Rayman Origins is a jungle. It has two big "themes" which are just the deep jungle and the open spaces with palm trees and geysers. Sorry, if there were more, I forgot. I only vaguely remember a few places.
In Rayman Legends, it's... also a jungle. However, similar to the improvements in the soundtrack, you also have more variation here. There's a swamp environment, an enchanted forest with moving roots, a medieval castle and the castle's ramparts during a siege. All of these themes look and feel noticeably different. Players can explore calm places, mysterious dark dungeons and get mixed up in a super dangerous situation, a siege where everything is on fire! This simply doesn't exist in Origins.
Here's another thing: Remember the first level? Yes, you do. You start out in the swamp where you notice a castle in the background and enter it. The first part of this first level alone is more memorable than any place in Origins, simply because the castle "landmark" and the fact that you can travel to it, enter it and explore it makes it feel more like an actual place, not "just a level".
Rayman Origins makes next to no effort to make "places" (aside from the Moskito segments where you travel between worlds), but Legends does this very well in a lot of worlds.
The added variation continues into later worlds. A bland desert (with instruments in the background, but still overwhelmingly a bland desert) becomes a magical beanstalk that you can climb to discover makeshift toad settlements and ruins of a castle in the sky. Compared to Origins' brown-yellow, this world has a beautiful color palette of green roots on purple, blue and yellow skies as the time of day changes. And people say Origins is somehow more colorful.
Fiesta de los Muertos on the other hand feels less interesting than its Origins counterpart. There are some beautiful decors here, but in the end it all sort of feels like the same theme, whereas in Origins you had a clear distinction between the cold & hot themes. Gameplay-wise the world feels stronger (with the focus on the digging & duck mechanics), and because of the hints of sadness in the music (because it's the Day of the Dead) I like it better, so overall I still prefer the Legends world, but purely for the theme I'd have to give it to Origins here.
Now for the water world, both games knocked it out of the park. Origins had some strong variation, going from the village to underwater, to the dark depths of the sea and the mysterious temple at the bottom (though it would be better if we could explore it).
Legends puts a cool spin on it, the sea is now polluted with trash from an underground base built by the Toads! Like some sort of spy movie, you travel through the hangar and a maze of dark tunnels and pipes to stealthily infiltrate the Toads' base, all while avoiding deadly lasers and searchlights.
It is here that you reach my favorite level in the game, Mansion of the Deep. I like it a lot because not only is its music one of the best tracks in the game, but the level is designed as a place: you get to see various rooms used by the Toads such as their barracks (tiny little beds), fish tanks where they've imprisoned a Teensy, and a luxury room which I've always thought was supposed to be a mini-casino? Similar to the Echoing Caves part 1 in Rayman 2, you have to explore different paths to hit switches and backtrack to the start. Here you turn off the power, to get access to a deeper part of the base. This changes the area drastically: everything becomes dark, more Toads come out and searchlights are activated to search for the intruder. Even those tiny little beds now become useful hiding spots that have a use gameplay-wise. Brilliantly designed, and there is nothing like this in Origins, not even its best levels come close.
Should I even write about Olympus Maximus? You already get the picture.
Winner: Rayman Legends
GAMEPLAY
I have a lot less to say here, but one thing a lot of the gameplay changes from Origins to Legends have in common is that they try to improve the flow of the gameplay. When I played Origins I often felt like the devs didn't know what the gameplay should be like: slow and precise or fast?
Now I like slow and precise gameplay, like Rayman 1, but the movement in UbiArt games isn't really made for this and it feels much more fun to run through everything. Often, that's what you did in Origins, but sometimes it stopped you in places where it felt annoying to stop.
For example, Rayman Origins has a bubblization mechanic, which requires you to stop moving to bounce on a dying enemy a second time to get extra lums. Often I felt frustrated at having to stop for this. Legends got rid of this mechanic, which was appreciated.
In similar fashion, it's well known that the air kick in Origins completely stops your momentum, and Rayman Legends fixed this. Your character's movement feels a LOT smoother as a result.
One thing I do not appreciate as much is the addition of Murfy levels. These actually slow down the gameplay. I guess these were fun in multiplayer on Wii U, but on other platforms they really weren't. There's also the duck transformation, which is completely unexpected and very funny when you first see it, but not very interesting outside of that. But it lasts only for one level.
On the other hand, Rayman Legends also adds various other gimmicks that I find pretty fun, like the stealth in the ocean world and digging in the food world.
A point that Origins fans often bring up is that it's more challenging, and this is true. However, some of this challenge seems to come from worse movement mechanics and less thought through level design...
Winner: Rayman Legends
STORY
Rayman Origins had a story that got scrapped last-minute, leaving many details in the game that lead absolutely nowhere, only serving to confuse players. The intro cutscene shows the microphone that explains how the grannies below heard the heroes snoring, but you can only tell that it's a microphone if you have read the scrapped text. Only then do you also know that the Magician put the microphone there. Only then do you understand the Magician's betrayal. Only then do you know
the Magician's identity. Otherwise, there is only confusion.
Rayman Legends has no story, hence, it has no such problem.
Winner: Rayman Legends
VARIOUS
Look. Rayman Origins has pig Latin. Rayman Legends does not.
Winner: Rayman Legends
IN CONCLUSION
A lot of my arguments are my own opinions, of course, but a lot are also objective facts. People aren't wrong for preferring Origins, they can prefer what they want, however they should also recognize that Rayman Legends is a clear improvement in many areas.
I've seen weird opinions being repeated in this community, like Legends "not being as colorful as Origins" (which tells me you didn't play the game past the castle area) or it being "Ubisoft formula" (maybe the game had too much content for you? That's fair, but the quality of it all is far above what we understand now as "ubisoft formula"), to which I say: take off your weird nostalgia glasses for this unfinished Rayman Legends prototype from 2011 and play the final game. It's pretty good.
Winner: Rayman Legends