While both games have their ups and downs, I slightly prefer Twilight Princess overall. Let's jump to the categories!
Controls: Twilight Princess
TP wins here because you could do much more, aiming with the Wiimote is arguably more fun than with an analog stick. Also there were more special sword attacks in TP. And we may not forget Epona >>> boat when it comes to moving. You get along with her much faster, you can override enemies and when you use an item you don't have to do a complete stop.
Overworld: Twilight Princess
While still not as good as other overworlds (especially aLttP and MM), TP's is much better than that of WW. Getting from A to B is much faster and there's at least some terrain variation instead of an always-the-same-looking boring opaque sea with comparably microscopic islands scattered throughout it. There were also more boring parts in WW in general, the Triforce quest was much more annoying than TP's shadow insects.
Dungeons: Twilight Princess
First, there's considerably more of them and second, they are themed better (although WW isn't that bad either). There's not that much backtracking (to give an example, I especially hated those three successive grappling hook ledges that you had to go down and up in Dragon Roost cavern and watch that same cutscene SIX times in a row). And I think that TP's dungeon had more 3D interaction, you had to go up and down much more (I don't mean regular stairs/floors but interaction in the same room).
Bosses/Enemies: Twilight Princess
Even though they are way too easy in both games for my taste, WW's are even easier than TP's. I think TP's are also more creative (for example Stallord). At least in TP there were some enemies that did a full heart damage (those insect things in the castle sewers are an example, and you only have 3 hearts at that point) and falling into the lava meant 2 hearts damage quite early in the game (can't remember how much it did in WW but probably only 1/4 or 1/2)
Items: Wind Waker
TP had cool items but most of them weren't put to use much outside of the dungeons they were found it (Spinner, Rod, Ball & Chain...). WW did things a lot better in that respect. Especially the grappling hook, Deku leaf and boomerang were put to good use. Oh, and WW was the last Zelda game in which you could use magic (like fire/ice/light arrows), too bad it was scrapped from TP and not re-introduced in SS.
Graphics: Twilight Princess
This is a rather personal thing, but I thought WW's were too over-saturated so that there isn't much change between areas. Cel-shading in general is OK for me but I really don't like the extreme body proportions in WW, I mean if your eyes are double the size of your feet then maybe you should see a doctor (jk). Some characters looked downright stupid IMO (for example Beedle, and I HATE that they imported him 1:1 into SS) Also the graphics made underwater action impossible which really sucks because I love water temples!
Unlike many others have said, I don't think that TP is too "brown" or "dull" at all. Some dungeons are darker, but they have to be to fit the atmosphere. But other places (like the Temple of Time or the spirit springs) are actually very bright and colourful, which makes a good contrast to other, darker areas, a contrast that is lost in WW because almost everything is mega bright and you can't make it even brighter to generate a contrast.
Music: Tie
Can't really decide here, both games had massive soundtracks with many new unique tracks. Most of the music also fit very well with the atmosphere at the respective moments. I also liked both new overworld tracks, maybe even slightly more than OoT's (but doesn't come close to the original Zelda theme
).
Story: Wind Waker
WW definitely had a more interesting storyline, things were explained better and Ganon didn't rush in in the last minute from out of nowhere.
NPCs: Wind Waker
WW easily wins here too, especially Zelda and Ganon played a much more active role than in TP and there were lots of other people (esp. in side quests) you could interact with. TP disappointed a bit here, I could never really feel much of a connection to Ilia at all and besides her most characters were quite bland and seen only 1-2 times, you couldn't even talk to most of the people in the town.