Time for my 2 cents
Graphics- While the cartoony style of WW was nice, the graphics (overall) were more appealing in TP. Not much explanation needed here.
Music- This is a very, very hard choice for me to make. One aspect of every Zelda game that stands out above the others is definitely the music. I can remember sooo much music from both games, from random stuff like Makar's theme from WW to the music that plays after you defeat a boss in TP. This is a tie. They're both fantastic in this aspect.
Story- Although both were very good, I'm going to go with WW. Ganondorf played the best role in this game, and I felt the ending was a lot more powerful than the ending in TP. I also feel that WW had a more memorable storyline. In WW I knew the whole time I was trying to save Link's little sister Aryll (omg I still remember her name!)
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, whereas in TP, I found myself wondering at the beginning "Who am I saving again? Oh yeah the girl who takes care of Epona." WW also had an insane plot twist. Finding out Tetra was Zelda freaked me out!
Characters- WW hands down. The characters are way more memorable than the few in TP. King of Red Lions, Makar, Medli, Tetra, the pirate gang, Aryll, etc. WW had the best cast of characters in any other Zelda game IMO. Only character that comes to mind in TP was Midna.
Controls/Gameplay- TP of course. I felt the Wii controls for the game were fantastic. The controls in WW were also solid, but I'd get bored out of my mind with WW's controls after playing through TP. The gameplay was more mast paced and energetic than in WW, especially with the horse riding. TP also had a wider variety of unique items.
Dungeons/Bosses- Once again TP hands down. As unique as some of the dungeons were in WW, I felt they were way too easy, but then again the ones in TP weren't much harder. The boss fights were also a lot less epic in scale when compared with the ones in TP.
Replay value- This goes to WW. After you beat TP once or twice, you don't have much reason to want to play through it again. I've personally played through the WW at least 4-5 times thanks to the nifty camera-thing that you take pictures with. I still haven't gotten all of the trophies yet! D: Oh yea, you aslo get to play as Link in his pajamas!
OVERALL- I'd say it's a tie. There are individual aspects that we love with each game. It all comes down to personal preference. My guess as to why WW is so popular in this thread is because you guys loved the story/characters much more than in TP. WW is a more memorable game. You can't deny that. But the TP fans loved the dungeons, graphics, and gameplay a lot more. TP was simply more fun than WW, and the darker mood is much more preferable than the light-hearted one in WW.
tl;dr: They're both amazing games, but I'm slightly leaning towards TP.