It really depends. There are some exceptions.
Which had games with the better setting?
Toss-up. This is likely the only thing Bethesda actually does well, but everyone does this one. Even the love-to-hate FF XIII had a solid setting if you ignore how it was presented in the story. An excellent setting is a bare-bones requirement of a good RPG.Everyone does this one well.
Which had games with the better music?
JRPGs. WRPGs are more inclined to treat music as wallpaper hangers. Not saying this is a hard and fast rule, but by and large JRPGs will skimp a bit on graphics and put the difference in music, while WRPGs will do the reverse.
Which had games with better game design (How the game works)?
JRPGs. With a few exceptions, WRPGs tend to cram things in like choice. Things on the cutting edge of game design which they aren't really ready for. The result is that WRPGs tend to be somewhat clunkier than JRPGs.
Which had games with the better combat gameplay?
WRPGs. Really, the problem with the JRPG is that very few of them have gotten past the random encounter. Combat and regular gameplay should be as seamless as possible. WRPGs tend to get this much better than JRPGs.
Which had games with the better story?
JRPGs. Again, with a few exceptions JRPGs are ABOUT telling a story, while WRPGs tend to be much more mechanical sandbox in nature...which doesn't lend itself well to traditional pacing or three-act structures.
