I am also putting up the original versions so you guys can compare:

Twister (Original Version):

Twister (Kingdom Hearts 3DS Version):

Calling (Original Version):

Calling (Kingdom Hearts 3DS Version):

Someday (Original Version):

Someday (Kingdom Hearts 3DS Version):

I never played The World Ends With You but considering offbeat the soundtrack seems, it seems like something really unique. I am now going to check it out.