Japanese character design is much more iconic. Western char design usually falls into a few categories for me:
-the bald space marine/crew-cut square-jawed military guy
-the basic 30 year old white guy with an average build, brown hair, and a face based off one of the game's designers
-googly-eyed, slightly creepy mascot characters
-(and for indie games) pixel art that resembles classic Japanese games
-women with man-jaws and big lips
-knights with huge pauldrons and bulky armor
There are some western designs I like (I think the Witcher games does a pretty decent job at aping realism while having a bit of style, Altair and his robes were pretty cool even if his game was lame) but on average they are just forgettable.
Of course, in the olden days, Japanese character design was even more iconic. How many iconic western character designs can you remember from the retro days? The MK ninjas, Crash, Earthworm Jim, uhh... even back in the early 80's, you had the Atari games with their realistically-proportioned stick figures, while Japanese devs opted for a more cartoony and expressive look.
And enemy designs, Japan is in a league of its own. Whether it be cartoony (the Slime from DQ) or horrific (Silent Hill) or just plain stylish (Monster Hunter)...