I have mixed feelings about both games; I mean, I love both of them, but I think that they do each have strengths and weaknesses. For full disclosure, I do not have a Game Cube, so I had to play the Wii version of Twilight Princess.
My personal preferences were as follows:
• Art Style - Twilight Princess. I can definitely understand why people could prefer Skyward Sword's style, but I did not. I loved the aesthetic choices that the developers made for TP; the eerie colors of the twilit provinces, the more realistic style, and the "dark" elements. By comparison, I felt that Skyward Sword's colors were too bright and "cartoonish". It didn't really work for me - I definitely prefer Twilight Princess's look and feel.
• Controls - Skyward Sword. Skyward Sword's motion controls were much more fine-tuned. I guess this makes sense since Twilight Princess isn't really supposed to BE a Wii game. I hate the fact that both games were made for right-handed players; I am left-handed and since Link is supposed to be left-handed, I just got annoyed that they reversed Twilight Princess. I think that they should have at least let you choose the handedness. Not that this really affected gameplay too much, but it's mostly the principle of the matter that irritates me. The stabbing and different sword stroke directions worked great for me, so I preferred Skyward Sword.
• Overworld - Twilight Princess. I didn't like Skyward Sword's overworld much; flying around was annoying and I'd rather be able to travel on the ground between the different areas rather than having to fly around between regions. While this makes sense for the plot (being that Link is from the sky) it made sense, but I didn't like the mechanic regardless. By contrast, I liked in Twilight Princess that you gradually unlocked more pieces of Hyrule Field, and there was a lot more regional variety. The map was large, but horse and wolf-travel made that not such a big deal. Even more importantly, night time existed in Twilight Princess. I love seeing day/night changes, which were completely missing in most of Skyward Sword.
• Dungeons - Twilight Princess. This was pretty much a tossup; both games have really good dungeons and really bad dungeons. The good - Lanayru Mining Facility, which is probably the best dungeon between both games. Also; Arbiter's Grounds and the Lakebed Temple, both of which I enjoyed greatly. The bad - Fire Sanctuary, which was boring and lame to me. I was so disappointed to find that there was a second fire temple in lieu of a shadow or ice temple, and nothing particularly interesting happened within the temple. To a lesser extent, the Sandship was a revamp of LMF with the timeshift stones, but I give it a pass because it is a decent dungeon and timeshift stones are still pretty creative. On the TP side, City in the Sky is the worst dungeon from either game. It is truly awful and if I could kill it with fire, I would. Overall, I went with Twilight Princess because there is more variety in themes and location.
• Music - Skyward Sword. This was a difficult choice, because I really love Twilight Princess's soundtrack. However, the orchestral quality of Skyward Sword made it much better than Twilight Princess's overall tracks. Particularly memorable are the desert tracks from Skyward Sword - the way the music changes when you activate timeshift stones is magical. In Twilight Princess, the tracks were still wonderful, but just didn't have that extra spark.
• Plot - Skyward Sword. I did like Twilight Princess's plot; especially helping Link's Ordon friends, the Zora Prince, and Midna's storyline. However, I think that the plot loses focus toward the end. After you gain access to the City in the Sky, Link's friends become completely irrelevant, and going to save Zelda from Ganon feels really contrived considering how little development and screentime either character has. By contrast, I liked Skyward Sword's prequel elements, and Zelda was a much more interesting and engaging character than her Twilight Princess counterpart. Ghirahim was also a much more involved villain than Zant, who pretty much just reverted into an insane hot mess for no reason. I also liked that the time travel element returned, which didn't appear in Twilight Princess.
• Enemies/Bosses - Skyward Sword. This goes hand in hand with the controls, but I think that Skyward Sword's boss battles are more varied and interesting; sword direction becomes an important element. In Twilight Princess, I felt that I pretty much either whacked the bejesus out of everything with the sword, or shot it in the eye with an arrow and then whacked the bejesus out of it with the sword. That being said, I did not appreciate the fact that 2 out of the 6 temples in Skyward Sword essentially didn't have a boss; rather, the boss was a character rather than an environment-specific entity that made sense relative to the temple. This was more obnoxious in Fire Sanctuary than Skyview; at least Skyview was a great introduction to Ghirahim. Also, The Imprisoned was awful, and made me not want to ever visit the Sealed Grounds in case it woke up.
• Overall - Twilight Princess. Like I said, I like many aspects of both games - it's just a matter of what you value in a game. I preferred the overall feel/atmosphere of Twilight Princess, the graphics, the regions, and the overworld. I don't think either game is bad, or either game is amazing; but I do think that both have an important place in the series and I would happily replay either one. It just comes down to personal preference, really.
My personal preferences were as follows:
• Art Style - Twilight Princess. I can definitely understand why people could prefer Skyward Sword's style, but I did not. I loved the aesthetic choices that the developers made for TP; the eerie colors of the twilit provinces, the more realistic style, and the "dark" elements. By comparison, I felt that Skyward Sword's colors were too bright and "cartoonish". It didn't really work for me - I definitely prefer Twilight Princess's look and feel.
• Controls - Skyward Sword. Skyward Sword's motion controls were much more fine-tuned. I guess this makes sense since Twilight Princess isn't really supposed to BE a Wii game. I hate the fact that both games were made for right-handed players; I am left-handed and since Link is supposed to be left-handed, I just got annoyed that they reversed Twilight Princess. I think that they should have at least let you choose the handedness. Not that this really affected gameplay too much, but it's mostly the principle of the matter that irritates me. The stabbing and different sword stroke directions worked great for me, so I preferred Skyward Sword.
• Overworld - Twilight Princess. I didn't like Skyward Sword's overworld much; flying around was annoying and I'd rather be able to travel on the ground between the different areas rather than having to fly around between regions. While this makes sense for the plot (being that Link is from the sky) it made sense, but I didn't like the mechanic regardless. By contrast, I liked in Twilight Princess that you gradually unlocked more pieces of Hyrule Field, and there was a lot more regional variety. The map was large, but horse and wolf-travel made that not such a big deal. Even more importantly, night time existed in Twilight Princess. I love seeing day/night changes, which were completely missing in most of Skyward Sword.
• Dungeons - Twilight Princess. This was pretty much a tossup; both games have really good dungeons and really bad dungeons. The good - Lanayru Mining Facility, which is probably the best dungeon between both games. Also; Arbiter's Grounds and the Lakebed Temple, both of which I enjoyed greatly. The bad - Fire Sanctuary, which was boring and lame to me. I was so disappointed to find that there was a second fire temple in lieu of a shadow or ice temple, and nothing particularly interesting happened within the temple. To a lesser extent, the Sandship was a revamp of LMF with the timeshift stones, but I give it a pass because it is a decent dungeon and timeshift stones are still pretty creative. On the TP side, City in the Sky is the worst dungeon from either game. It is truly awful and if I could kill it with fire, I would. Overall, I went with Twilight Princess because there is more variety in themes and location.
• Music - Skyward Sword. This was a difficult choice, because I really love Twilight Princess's soundtrack. However, the orchestral quality of Skyward Sword made it much better than Twilight Princess's overall tracks. Particularly memorable are the desert tracks from Skyward Sword - the way the music changes when you activate timeshift stones is magical. In Twilight Princess, the tracks were still wonderful, but just didn't have that extra spark.
• Plot - Skyward Sword. I did like Twilight Princess's plot; especially helping Link's Ordon friends, the Zora Prince, and Midna's storyline. However, I think that the plot loses focus toward the end. After you gain access to the City in the Sky, Link's friends become completely irrelevant, and going to save Zelda from Ganon feels really contrived considering how little development and screentime either character has. By contrast, I liked Skyward Sword's prequel elements, and Zelda was a much more interesting and engaging character than her Twilight Princess counterpart. Ghirahim was also a much more involved villain than Zant, who pretty much just reverted into an insane hot mess for no reason. I also liked that the time travel element returned, which didn't appear in Twilight Princess.
• Enemies/Bosses - Skyward Sword. This goes hand in hand with the controls, but I think that Skyward Sword's boss battles are more varied and interesting; sword direction becomes an important element. In Twilight Princess, I felt that I pretty much either whacked the bejesus out of everything with the sword, or shot it in the eye with an arrow and then whacked the bejesus out of it with the sword. That being said, I did not appreciate the fact that 2 out of the 6 temples in Skyward Sword essentially didn't have a boss; rather, the boss was a character rather than an environment-specific entity that made sense relative to the temple. This was more obnoxious in Fire Sanctuary than Skyview; at least Skyview was a great introduction to Ghirahim. Also, The Imprisoned was awful, and made me not want to ever visit the Sealed Grounds in case it woke up.
• Overall - Twilight Princess. Like I said, I like many aspects of both games - it's just a matter of what you value in a game. I preferred the overall feel/atmosphere of Twilight Princess, the graphics, the regions, and the overworld. I don't think either game is bad, or either game is amazing; but I do think that both have an important place in the series and I would happily replay either one. It just comes down to personal preference, really.