Controls - Skyward Sword has way better motion controls hands down, but as for combat I loved the many upgrades you got in Twilight Princess like flipping over an opponent or shield bashing, ect. So while Skyward Swords had better controls, Twilight Princess has more "moves" So I would say either tie or Twilight Princess wins. Though I hated being a wolf.

Graphics - don't care, both had great styles

Story - I think Twilight Princess wins. While origin stories are always fun and it was a greatly told, I think that Twilights had a more engaging exciting story. You got to find out what happened to Ganondorf after Ocarina, learn about twilight world, ect.

Side Quests - Have to give this to SS. Even though probably had less, they were more intertwined in the game. The Twilight ones were just there and random. SS made them be from people you knew and for good reasons, ect. Also loved upgrading things like weapons and items.

Items - Hmm, been a while since played either game, so have to think on which items each had. Double claw, Spinner and giant ball and chain is what I remember on TP. They were all super cool even though they really didn't get much use after getting them. Can't think of an AMAZING item on SS, but they were implemented well throughout the game and never became a one trick pony. So do I reward the game that had cooler items or used them more thourougly and better? Gonna go with #2, SS. I prefer items being useful the whole game and unlocking areas you couldn't go before ect than an item being a one trick pony in a dungeon.

Dungeons - Another weird one. Only for the sole fact that skyward sword almost felt like the entire game was a dungeon. There really didnt' feel like an overworld. You were constantly doing dungeony stuff everywhere. So its kind of hard to recall what was a dungeon and not. But overall even the overworld parts I think were done as well as any TP dungeon, so SS still wins easy.

Characters - Hands down TP, imo. Never really cared for anyone in SS, not even Zelda. Only liked Link. While may not be many more in TP I loved, I did love Zelda & link for sure so that's already 2. Ganondorf is always a plus, and I think Zent was a better villian in terms of hating and being scary/creepy. SS boss felt like a pedophile. Though the final boss was cool.

Boss fights - Hands down TP, no contest. No Zelda game ever game me an awesome of final boss as this game did. Then you have other battles like the spinner and bone dragon and it's just amazing. While SS might have one of the coolest bosses ever in the 6 handed giant soldier, one boss isn't enough to beat all of TP's amazing fights. Even sub bosses ruled in TP. Remember when going to temple first time and fighting your first huge armored soldier guy. Amazing.

Don't want to pick a winner, just giving my thoughts on each category.

This also confuses me a bit, sure it was built around Gamecube at first, but the thing is it did release on Wii first, that's the reason why I don't know for which gen to count it.