The exhibits are very similar, but
the Yokohama branch wins because 1) it's in the center of Yokohama's waterfront district, rather than off in the middle of nowhere, and 2) they have a much better food court (Noodle Bazaar - World Noodles Road), with eight different booths serving noodle dishes from all over the world.
Also you can go to the Cupnoodles Museum and the
Shin-Yokohama Ramen Museum on the same day, although they're about 30-40 minutes apart.