I usually place The Wind Waker at #2 and Twilight Princess at #3 on my "Favorite Zelda Games List" so I like them both a lot and almost equally. Here's my comparison:
Gameplay
Both are almost equal gameplay-wise (in my eyes). For me, transportation was undoubtedly better in TP. I much prefered riding Epona instead of sailing throughout a vast, empty ocean with nothing really to do other than go forward. The fact that you could use items and your sword, while horseback made it even better. However, TWW had more exploration, which is what the Zelda series is all about. I can't really compare the motion controls of the Wii version of TP since I have the GC version, but the contols for both TWW and TP to be equal. I think TP had some innovative, fun items like the spinner, double clawshot and dominion rod but there weren't really any items in TWW that made me think "WOW!" Overall, the gameplay was great for both games.
Atmosphere/Graphics
I think that TWW is full of light-hearted whimsy and vibrance while TP was dulled down with its use of muddy colors, horrible textures and an unoriginal art style. Don't get me wrong, I do appreciate TP's grim, dark graphics, but I prefer TWW's so much more. TWW's atmosphere was full of charm and originality, but TP's graphics were just like any other game out there, just with worse textures. However, both graphical styles compliment their respective games and fit the premise perfectly. Overall, I thought the tone and graphics in TWW were the best in the series.
Story
I think TWW's story is far superior to TP's. Although TP's story was more intricate, deeper and more emotional, it felt more like a random (yet linear) set of events that just seemed to happen one after another. Right after you do one task, you are sent to do the next. In TP, it just felt like I was being pushed to go to the next part of the game instead of being able to take my time and explore the world. It just didn't have a sense of freedom. TWW excelled at freedom. Although the story was shorter and not as detailed as TP's, TWW's story felt like more of an adventure. I was more in control, which is something I need in a Zelda game.
Many of TP's events were also unnecessary. Ilia's memory loss, Epona's rampage, and Midna's sickness (among others) felt like they were just thrown in there to add more to the story, even though they had nothing to do with anything. Many of these events would work wonderfully as sidequests, but for some reason the developers thought it was necessary to add these random, pointless events into the main story. TWW didn't really have any useless events with little revelance to the story (That I can think of).
Music
There's not a LOT to be said about the music, and of course, it's only my opinion. I really liked TWW's soundtrack. I loved the use of the pan flute in many themes and I think that added a certain charm to the game. The Dragon Roost Island theme and the Legendary Hero Theme are both in my top 5 tracks of the series. TP's soundtrack was average in my opinion. It did have some standouts (Midna's Lament, Hidden Village, Gerudo Desert, opening theme, among a few others), but most of the soundtrack was kind of forgettable. The music did set the tones for their respective locations but still were just okay. They seemed a bit hollow and tinny as well.
Characters
This one's a bit of a toughy. I think TP's characters are incredible but I loved the different races of TWW. If I'm forced to choose, I prefer TP's characters. They showed more emotions and I cared for them more than TWW's. They were also dynamic and showed different sides to their personalities. Midna in particular was brilliantly crafted. TWW's characters were cute though, and I like them for that. However, I prefered TWW's Rito and Korok races over TP's Goron, Zora, Ooccoo and Twili races.
Technical aspects aside, I think The Wind Waker is just overall a more fun, enjoyable game. I'm in the middle of playing Twilight Princess for the third time but I feel like ditching the game to play Ocarina of Time instead, which is odd because I usually place OoT lower than TP on my favorite Zelda Games list. They're all masterpieces though. You can't go wrong with any Zelda game.