I don't know if I'll really add more to this than has already been said, but seeing as I'm an American who was raised on Western Animation and now support Eastern Animation more, I feel as if I have something to say on this.
I was happy to see two things listed previously in this thread, Perfect Blue and Ghost in the Shell. While I'm sure most people are at least fundamentally aware of Ghost, it's up in the air how many people know anything about Perfect Blue. (If you're not, please check it out on Wikipedia)
The main problem to start with this debate is that you're in short comparing a deeper cultural divide than you'd think. First, we have to acknowledge that the level of target for Western Animation is vastly different due to greater cultural handicaps than that of Japan. When Princess Mononoke was being released in the States, there was a bit of controversy as to whether or not it was proper for Disney to hold the rights to it due to the violence level in the movie. This is part of the base cultural divide between the East and the West. While there is some "innocence" to children in Asia, the driving force of Eastern Animation comes from Japan where the "sheltering" of children isn't as deep as it is here in the States at least.
What this really drives at is why Western Animation as a whole seems to constantly yield similar titles. As commented in the video, Disney is primarily known for Princess movies. Even looking back on my childhood, the only movies I felt really stood out or captured my imagination weren't from Disney because I was a boy. Instead, I remember fondly things like An American Tale : Fievel Goes West, The Secret of Nimh, and Titan AE (though released in my teens.) At best, for relation to myself, Disney had The Sword in the Stone and television shows such as Chip and Dale Rescue Rangers, Tail Spin, or Gummy Bears. But looking into my teens, Western Animation seemingly lost all appeal or connection to me.
Instead, it was at this point where Eastern Animation took up the mantel starting with a friend letting me borrow Akira and Ninja Scroll. Soon afterward I got hooked on the epic feel of the space soap which was Gundam 0079 and small titles like Pet Shop of Horrors or those now obscure US Manga and Urban Vision title releases such as Psycho Diver or Twilight of the Dark Masters.
Heck, I remember Sputnik7.com when they had their license to stream US Manga titles like Wings of the Royal Space Force: The Wings of Honnêamise or Mad Bull 34.
Now, I know this is me sort of droning on about my experiences, but I'm trying to establish a timeline. For most people, I assume, the connection to a certain animation style seemingly comes from the disconnection of another, and I believe that is why this topic is inherently flawed from the begging. It is reasonable to say that with what we have widely available, Western Animation is probably better for a domestic market in the West currently for the ages of 3-10 years of age. However, even at the ages of 5-8 you enter a world of Pokemon, Yugioh, Digimon, and a slew of others which have equal appeal to children. But when it comes to the teen market upwards to any adult level, Easter Animation meets what the West by and large refuses to try.
Now, most of the void in the market comes from the still long standing opinion that Animation is for children, with the exception of children movies laced with humor only the parents are supposed to understand thus allowing them to not want to drink bleach by having to sit through them with their children. It's taken over 60 years for Comic books to finally start getting real credit as a legitimate art form in more ways than one, and I assume it will still be years off for the West to fully acknowledge the potential of Animation as a true entertainment medium.
Going back to the beginning, Perfect Blue is a bold example of this line of thinking and recognition that the West has yet to fully adopt. Blue is a title which explores vanity, obsession, sexual expression, rape, murder, the effects of modern media and entertainment, and our inner psychological flaws we each do well to keep hidden from others. Now, it doesn't overly drown you in all of theses, but there is enough there to get you thinking and all done on a fair budget to bring a very powerful book to life.
I guess in the end, it isn't so much that I choose Eastern Animation to be the better of Western; It is that I choose the artistic freedoms and acceptance of the East over the West as a good fit for my personal diversity of taste when it comes to entertainment.