Jrpg for all categories

This. I've never been able to enjoy any aspect of a JRPG. In fact I used to dislike all RPGs because i thought they were all like JRPGs until a friend introduced me to elder scrolls and mass effect. Haven't looked back. 

Depends.
Most WRPG settings are the typical middle/dark ages settings. Those bore me, I like skyrim cause its nordic. JRPG settings tend to be more imaginative.

They both have good music. I would say WRPG's tend to fit the game better in their musical choices. While JRPGs tend to go for music that is good outside of the game. Essentially, I only listen to WRPG music when I want to get in the same mood as I do when playing the game, while I listen to JRPG music more at different times for instance my wakeup alarms include: Persona Music and Kingdom Hearts music.

Its a toss up here too. I don't think good game design is limited by its genre.

Depends on the combat. I prefer JRPG combat simply because WRPG combat tends to be more restrictive.

I don't think story is limited to genre. That being said jRPG storys tend to be more imaginative or at least have more out of genre tropes, while WRPG stories tend to more conservative and have mythological tropes like goblins, trolls, elves... etc. In that regard I prefer jRPGs.

WRPG clear winner for everything but music. I'd give it to JRPG, if only for all the classic 16-bit midi tunes they produced.

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I guess JRPG since my favorites are the Souls series and Ni No Kuni.
Baldur's gate and Dragon age follow a bit further down the list for favorite WRPGs

Which had games with the better setting?

I give a small edge to JRPGs, with settings like Midgar, Ivalice, Figaro Castle, or present-day Japan (SMT) or America (Earthbound, although very stylized). WRPGs have some interesting settings but too many of them are rehashes of stock Tolkien or George R. R. Martin tropes, neither of which interests me.

Which had games with the better music?

JRPGs easily. I can recognize the tunes in almost every Japanese RPG I've played. Beyond a few licensed/public domain tunes in Fallout 3 or New Vegas I couldn't even pick out any WRPG's soundtrack..

Which had games with better game design (How the game works)?

Hard saying. JRPGs tend to feel less like $60 betas (looking at you, Bethesda!). On the other hand, lot of WRPGs are more open-ended and I liked the game mechanics in New Vegas in particular.

Which had games with the better combat gameplay?

JRPGs by a mile here. Bigger variety in play. WRPGs tend to be all action RPGs these days, and JRPGs in general do better even as action RPGs.  Bioware's games are unwieldy, Bethesda's games feel like slap fights against paper dolls.

Which had games with the better story?

JRPGs tend towards more nonsensical plots, but to me that isn't a bad thing. WRPGs have more structured, focused plots, I guess. Both approaches are good if done right.

So overall, I prefer Japanese RPGs over Western RPGs.

"Jrpgs when they try to be Wrpgs.... in other words the soul series."

- I disagree since this series had some of the worst game design I had ever seen, like, on par with shitty indie games

naturally JRPG/WRPG just comes down to preference and well, the games themselves (hard to make blanket-statements over an entire genre), but

Which had games with the better setting? - JRPG settings tend to be more interesting

Which had games with the better music? - JRPGs for SURE, western soundtracks tend to be bland and treated more like background music you hardly hear except in exciting scenes (kinda like in movies) and therefore usually make little to no impression on the player and aren't very hype

Which had games with better game design (How the game works)? - generally WRPGs seem to do better in this (too many cliches/poor balancing/grinding issues in JRPGs I think)

Which had games with the better combat gameplay? - JRPGs tend to be more creative and successful on this front, IMO

Which had games with the better story? - same as above, but highly comes down to preference

note that I'm of the opinion that JRPGs lately have generally gotten kinda worse, maybe even more generic and bleh, like for some games it's all about fan service and tropes and shit

not that WRPGs are really doing anything impressive either and don't have their fair share of (slightly more realistic) boobs, but still

Which had games with the better setting?
JRPG - I think the worlds are far more vivid.

Which had games with the better music?
JRPG - No contest.

Which had games with better game design (How the game works)?
Draw - Hard to compare really. JRPGs are a bit too simple for some, but they're extremely polished.

Which had games with the better combat gameplay?
Draw - All depends what you're into. Turn based (or variations) vs real time. I love Final Fantasy XIII's system and I love engaging dragons in Skyrim.

Which had games with the better story?
JRPG - Although silly and cliche at times, I think JRPGs tend to have much stronger stories and make better use of cutscenes.