Looks like I need to make a list for this one:
Mario Galaxy: I'm a fan of the space background and the music (always have the Bowser's Inside Story final boss track set to max because it captures the sense of a cosmic battle).
Kalos Pokemon League: Yes, it uses the same main platform from the normal version, but I'm just a fan of both versions overall because of the ballroom setting complete with the excellent music options (one of which reminds of Professor Layton).
Coliseum: It still captures the Coliseum feel even without the walkouts, and compared to Arena Ferox, it feels much more alive. It's another stage that I like the music for.
Palutena's Temple: Because it's layout is just like the real Final Destination, and it has one of my favorite tracks in the game.
Boxing Ring: Again, still captures the same feel like its normal version but without the walk-offs, and has some great music.
Gaur Plains: Not a fan of the normal version because of the gap in the middle (though I'm aware they were trying to recreate the canyon feel), but I love the Omega version. The layout feels very similar to the real Final Destination with the only difference being the thin pillar in the middle, and yet again, it has some great music.
Pirate Ship: Easily my favorite Omega stage. I absolutely love how the stage completely stages from the ship to the tower. Fighting on the tower feels like a lot of fun to be honest, and my favorite detail is that the original Pirate Ship appears in the background from time to time (and when I mean the original, I'm talking about the one straight from Windwaker, not the redesigned one we got in Smash). I was also surprised at first that the main "pole" is actually behind the main stage so that you can easily jump underneath, but I liked that since it felt more playable for a competitive setting.
Suzaku Castle: My second favorite Omega stage. Not a big fan of the normal version because it feels rater unplayable with half of the stage having little platforms while the other half involving a walkoff. The Omega version feels like you are actually fighting in a Street Fighter match. Even the layout is pretty similar to the real Final Destination minus the fact that it is walled at around the bottom end. And yet again, I like playing this stage for the music (particularly the Ryu themes).