As a person who didn't grow up around Korean and Japanese things and merely got into them as a teen and up, here are my opinions based on observation:

Best Food: Korea (less bland)
Best Oral Language: Korea (more rhythmic)
Best Written Language: Japan (because of the characters still being used )
Best Films: Japan (some Korean films seem to be copies of other films from other places)
Best Music: Korea
Best Fashion: Japan
Best Cartoons/Comics: Korea (the illustration is more colorful and more detailed)

i never went to korea or japan..
but i heard japan are more clean and more forward..
i think japan wins all..
i dunno why ppl said korea fashion are better but a lots korean fashion are copy from western and japanese..
japanese music are better..kpop do not have the originality..even though i addicted listening to kpop now..korean music just like the continuous of american or japanese..
about drama..of course jdrama wins..
and cartoon..anime wins again..
overall must be japan..
i always heard that korea is next japan..so japan is more forward..

Food:
I pick Japan! I love sushi <3 & I love their yummy snacks!
Fashion:
Hmm....I'd pick Korean fashion, though they are really similiar...except Japan projects the harajuku & emo style best, which I don't dress like.
Animation (Anime/Cartoons):
Definitely Japan! I grew up watching Japanese animation, like DBZ & Street Fighter.
Music:
I can't choose. I love Korean music but I also love Japanese music too!
Drama Series:
I grew up watching Korean dramas. It was not too long ago when I started watching Japanese dramas. Each has their own good dramas but I'd have to pick Korean dramas.
Enviroment:
Ummm...both? I think Korea & Japan are very attractive with the islands & tall buildings, traffic & huge oceans of people.

Kdrama is definitely the best. Korean actors are better looking than Japanese actors. For food, Chinese is the best, Korean and Japanese are even.

Food: Japan. mybe bcoz i never have a chance to eat korean food.

Fashion: Korea. they hv a simple fashion style.

Animation (Anime/Cartoons): i don't like both. coz i never watch anime. but for cartoon, i prefer japan. they r cute!

Music: Korea coz i love 'em. FT island, BB, SHINee, etc.

Drama Serials: Korea&Japan both of them produce lots of great drama and movies and i could not choose one.

Enviroment: Korea&Japan. wonderful country.

food: Japan

music: Korean

dramas/movies: i havent watched much, but id say tie, although japan has great mangas that have been turned into great dramas, i like the acting of koreans better.

fashion: makeup and clothing wise korea

rather visit: japan!